There isn't even such a thing as an "evolutionist" any more than there are "gravitationists". Just people who accept scientific facts and people who do not.
The VAST majority of theists in the world accept evolution because it is established science supported by a century and a half of hard evidence. Science denialists are mostly found in uneducation Third World nations and, unfortunately, among ignorant American fundamentalists.
The way I see it, the world is not black and white. There is a place in between for people who believe in both Darwin's theory of evolution and in a deity. Christianity dictates that the way to find salvation is to ask forgiveness from The Lord, not believe everything in the Bible should be taken literally. There is room for interpretation. Perhaps, 7 days in God's time is not the same as time on Earth. Maybe God is continuing to shape and grow us, just as farmers tend to their crops and watch them flourish.
I would like to call myself both of those. While I think there is a definite supreme being, and this being created everything, I think there are limitless options for him/her/it to do so. It could be spontaneous existence, although I think this is probably irrational. Things just don't come into existence randomly. (I know, I know. How do I prove the existence of God then? That's a different conversation entirely, that I don't feel like typing out here.) Evolution is a much more sound theory, that explains why humans are getting taller, bigger, etc. And other animals, too, are changing as we know it. Now, I don't think that we evolved from monkeys, but that too could be incorrect. My point is that the two terms are not mutually exclusive.
Many people make the mistake of assuming that you cannot believe in evolution if you believe in a God, or in any gods. This is a mistake, because no matter which version of the Holy Scripture you read (maybe the Old Testament, Torah or Qur'an to name a few) it does not specify how God/G-d/Allah, made the world. It says He made the world, but doesn't talk about how. He kind of left that up to our imagination. This is where you could argue that He created and developed the world through things such as the big bang and evolution - certainly the order things happened in the holy scripture and evolution seem to match up more or less. Also, the actual translation of Genesis from Hebrew, is "God created the world in 6 periods of time", NOT "God created the world in 6 days". The latter is actually a mistranslation, from the original word pronounced "dias" (apparently). I'm of the opinion that it doesn't matter how you believe God/G-d/Allah created the world, as long as you believe He did!
I am living proof of this fact. There is hard evidence for evolution and those who do not accept it are, forgive me, in denial. There is fact to this, and there is no reason for it to be considered blasphemy or something. So yes, it is perfectly feasible to be a theist and evolutionist. As much as some people may think us to be mindless irrational animals who believe in superstition, we are not.
Of course it's possible to be both - King David was both a great man and a murderer. The problem is simply that evolution is bogus, the mother of all junk science, and there's no good reason for anybody to buy into nonsense. It's very clever nonsense, mind you, but nonsense all the same, our generation's version of the Ptolemaic orbits of the planets.
The Catholic Church officially supports evolution, and there is no doubt that the Pope is a theist. Worldwide, opposition to evolution is only significant in the United States, and in the U.S. Mainly in the Bible Belt. It's an odd artifact of a particular religious belief and is unrelated to religious belief in general.
A "Theist" is someone who believes in a God(s) or Supernatural being(s). There may be a religion out there that actually thinks their God was only responsible for certain things as opposed to simply everything. So, my answer would be yes, it is possible, however most modern religions wouldn't have it as a belief as it is opposing their view/belief.
Religion is controversial, but also seems to state that your god/goddess/deity created everything. I believe you can think religion has good morals, such as forgiveness, but if you believe in religion, you do not get to pick and choose what parts you will and won't follow. Being religionless doesn't not make you someone without morals, morals that may be supported by certain religions, it is just something there is often deemed as bad. You can believe in science, or religion, but not both.