This is a complex subject and there are many theories of evolution, not just one. Nonetheless the answer is that a Catholic may believe in evolution if the theory does not deny any of the truths of faith. Science and faith don't contradict each other, because God made both. If there is a seeming contradiction is because we have not reached the proper depth. In particular, the following truths of faith must be preserved and not denied in any way:

1. God created the universe out of nothing. It was not a "chance" event.
2. Human beings are generated from two parents: Adam and Eve.
3. God not only created the universe, but his providence is continually active in the universe.
4. The human soul is created immediately by God.

A Catholic may also choose not to believe in a theory of evolution. Most of the evolution theories usually deny one of the points above, and most of them consider the human person as if it consisted only in the body. The truth is that a human person consists in both, a body and a soul.

Another point that is usually denied is that we come from two parents: Adam and Eve. Adam and Eve are the first human beings from which we were generated, because they are the first beings with a human soul. The body may or may not have evolved from lower animal forms, but the fact is that Adam and Eve were the first human beings from which we descend. For more information you can read the Encyclical Humani Generis by Pope Pius XII.