Based on the number of people who actually apply to agencies as a percentage of the total Christian population in any given country, I can’t imagine this is a question that is asked by very many people.In fact, I rather suspect that the inverse is more often said, as a statement: “I’m not a missionary” or “I can’t be a missionary” or “I’m not called to be a missionary.” I have argued before that not everyone is a missionary: 
Not everyone is a missionary: what we look for 
The article in which I agree with Eddie on who can be a missionary 
Single vs Complex Culture Crossing; or, we are not all missionaries However, what I’m really arguing in those posts is this: that ‘missionary’ is a particular role. If not everyone is a missionary, can I be one? Who is a missionary, biblically speaking? That’s hard to answer, since Missionary isn’t used in the Bible at all. It’s an English word, derived from the Latin mitto, a translation of the Greek apostolos. The Oxford English Dictionary says it was first used in 1598; by 1729 it was broadly used in association with the Biblical sense. So if “missionary” comes from apostollo, is a missionary an apostle? The two words are related by translation: the Greek apostollos was used in classical Greek impersonally to refer to something sent (e.g. an army sent). Josephus used it to refer to Jewish emissaries sent to Rome to petition Caesar. Apostolo is used hundreds of times in the LXX (Septuagint) as an equivalent of the Hebrew word for “send.” However, in the New Testament apostollo is used most frequently to refer to a specific group: mainly those in leadership, and specifically to the Twelve. Yet while admittedly the evidence is a little thin, it doesn’t seem to me to be limited to the Twelve. The Apostles undertook to replace Judas (Acts 1). Paul calls himself an apostle, and says in Ephesians 4 and 1 Corinthians 12 that “these are the gifts Christ gave to the church: the apostles, the prophets, the evangelists, and the pastors and teachers.” It doesn’t make sense to me to think we still have pastors, teachers and evangelists today and not the others (apostles and prophets).  But you should know others argue “apostle” ended with the early church; that “apostles” amongst other things had to be eyewitnesses to Christ (and Paul does make the case he is an eyewitness as one of his proofs). A colleague sent the following list of times in Scripture when “apostles” didn’t mean the Twelve, helpful:

• A great prototype for our kind of apostle, Barnabas: “But when the apostles Barnabas and Paul…” (Acts 14:14)
• Most debated, Junia (a clearly female name), who was “outstanding among the apostles.” (Romans 16:7) 
• Andronicus – same description, in Romans 16:7
• James: “But I saw none of the other apostles except James the Lord’s brother.” (Galatians 1:19 ESV) ”From the form of this phrase it would appear that James, the Lord’s brother, was considered to be an Apostle.”
• Others in Paul’s team: “We were not looking for praise from people, not from you or anyone else, even though as apostles of Christ we could have asserted our authority” (1 Thessalonians 2:6). (None of the 12 were with Paul in Thessalonica.) What is an “apostle”? This is really the question we need to ask, since it will drive our understanding of the word “missionary.”
• An apostle appears to be one chosen–and by God, not men. In Acts 1, they asked God for direction and cast lots. In Romans 1:1, Paul declares himself “chosen by God.” In Colossians 1:1 he says “chosen by the will of God”; in 1 Timothy 1 he says “appointed by the command of God.” In Galatians 1 Paul makes the point that he was not appointed by a group of people or authority, but by God himself.
• An apostle appears to be one who is sent for a purpose. In Romans 1, Paul says “sent out to preach…” In 2 Timothy 1 he says, “I have been sent out to tell others about the life he has promised through faith in Christ.”
• An apostle appears to be one sent to a specific group. Paul declares he is sent to the Gentiles (Romans 1:1, 11:13); he also describes Peter as “the apostle to the Jews” (Galatians 2:8).
• An apostle is not always understood to be an apostle. Because some don’t think he is an apostle, Paul suggests proofs he is. In 1 Corinthians 9:1 he points to the fact that he had seen the Lord, and suggests that “because of my work, you belong to the Lord” as evidence (9:2). In 2 Corinthians 12:12 he points to the signs, wonders and miracles he performed as proofs.
• Maybe, an apostle can also be other things: Paul says in 2 Timothy 1:11 that he is a preacher, an apostle, and a teacher; is he distinguishing between these roles? Let’s ask again: is a missionary an apostle? With a non-Biblical word, we can make “missionary” mean whatever we want it to–and we have. By “missionary” some mean “I go to a distant place and proclaim the Gospel, make disciples, baptize”–and this is permitted because we’re commanded in Matthew 28 to do precisely that. This is the sense those who argue “everyone is a missionary” use the word in. If someone goes to be a worship leader, a pastor, an English teacher, a business-starter in a distant place, and through that attempts to proclaim the Gospel and make disciples–this is “going on mission.” That’s a worthy thing. It is obedience to Matthew 28. On the other hand, if we say “missionary” is one “called by God and sent for the specific task of proclaiming the Gospel and planting the church”–now we are verging on equating missionary with apostle, in my book. “Can I be a missionary?” in this sense? I’d tread a little more lightly. I don’t know all of what the apostolic role means, but one thing seems clear: one does not simply choose it. To be an apostle is not just to go, but to be sent; and not just to be sent, but to be chosen; and not just to be chosen by men, but chosen by God. This is ground that we ought to enter with some fear and trembling. To be an apostle seems to be taking spiritual responsibility for others (Philemon 1:19). It seems to be taking responsibility for places no one has gotten to (Romans 15). It seems to be taking responsibility for all within an area, not just a handful (Acts 19). It is maintaining relationships and continuing to mentor over long periods of time (1 Timothy 1:2). In passing, let me dispense with the idea of an apostle as a kind of “rank.” While 1 Corinthians makes some kind of ordered list (with apostles placed first), in other places the list is given without any sort of ranking, and still in other places Paul made clear that all parts of the body are needed and equal before the Lord. Jesus himself said those who would be first in the Kingdom must be the servant of all. One more time – can I be a missionary? (or, can I be an apostle?) – I think the answer for anyone is “yes” – anyone can be (don’t prejudge whether someone is or not), but not everyone is (depending on how it is defined). And you can’t decide to take on the apostolic role on your own; you can’t “send yourself.” You need to first place yourself in a position before the Lord of saying “Here am I, send me.” Then, I think you need a clear sense of being sent–one that is confirmed by others (even if it isn’t always widely confirmed!). I know this flies in the face of what some have said (“we are all sent”) and particularly what Eddie Arthur has argued (whom I very much respect, and generally agree with–and I think he’d agree with me in this post). I think in this I’ve balanced the two ideas and delineated between the two. Am I called? I can’t answer that for you–but let me suggest perhaps the strongest initial signal of God’s calling is the willingness to “go on mission” even if you are not “sent.” In my experience very few are willing to “go” – so few that I suspect a strong correlation between “I want to go” and “God has sent me.” If you’re asking the question, “Can I be a missionary,” it’s a pretty good indicator to me the answer will be “Yes.” See also ”Are we all missionaries?” Rollin Grams. (“No.”) “Are all Christians called to be missionaries?” Eddie Arthur. (“Yes.”) “What do words mean?” Eddie Arthur (also on the complexities of how we define “missionary”) I’m not a theologian by degree; I’m just a lay activist for missions. I welcome comments, thoughts and critiques.