"Can I be a missionary?" 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."
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).
There are times in Scripture when "apostle" didn't mean one of the Twelve:
What is an "apostle"? This is really the question we need to ask, since it will drive our understanding of the word "missionary."
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."