Is it possible to be a scientist and a Christian?
Yes: all kinds of people can suffer delusions, scientists are not exempt.
The question usually comes up in the context of scientific scepticism. Scientists who are Christians usually compartmentalise their beliefs - following scientific method when they practice science and suspending it when they practice Christianity. Often they will denote some areas of knowledge as "outside science" or "unknowable to science" as a way of jusifying this. The challenge they face is in showing that their Christian beliefs are scientifically sound.
This produces some problems:
Amongst other things, Christians must believe in the God of the Bible, the Virgin birth, bodily resurrection of Christ, who is the Son of God, and God, the immortal soul, and salvation (via the crucifiction). This also means a belief in the continuation of the person (as a soul) after death, heaven, hell, and salvation. Disbelief in any of these things stops you from being a Christian. (If you disagree, then you are also at odds with most Christians.)
Scientists are supposed to accept empirical realism as the path to truth, or, at least, less untruth. Christians are supposed to accept the Bible, particularly the New testament, as the revealed truth of God, ahead of empirical discoveries. This is a basic point of epistimology which forms the main problem with attempts to reconcile science with religion. It is difficult to see how these can be reconciled without resorting to compartmentalization.