Answer:
Yes, determinism and existentialism are compatible. You have to remember that many people think that free will and determinism are compatible (compatiblism). However, existentialism seems to accept taking responsibility for your own actions, and radical free will. However, a closer look at existentialism will reveal that existentialist philosophers (like Nietzsche) generally hold the notion of a will that is not influenced by any sort of outside force, as is posited in libertarian free will, is a rather absurd notion. Also the notion that our existence precedes our essence, an existentialist view, seems to say, at least in part, that we do not have control over every part of our lives, which would support determinism and existentialist compatibility.