It is indeed possible. Magic is the understanding and application of natural processes and cycles into daily life. Philosophically both practices involve understanding, connecting with, and calling for assistance from higher or enlightened influences or beings. One can call on the image and idea of Christ (or Christ-consciousness), the archangels and other figures of the heavenly host, and use Christian symbols of protection and will quite easily.
The main sticking point is in personal philosophy, especially when it comes to how strictly you feel you need to stick to the tenets of the Church denomination you follow. For example Pentecostal or Protestant churches might be more relaxed about the idea than, say, Roman Catholic.
In the end, it boils down to you and what you are comfortable with. There is enough overlap to marry the two practices together in a few different ways. So study both paths and see how your own personal understandings and philosophy reconcile the two.
I guess, I am Roman Catholic, and still believe this is sinful, but the temptation was too much. In fact, i haven't practiced since march! I just try to keep my witchcraft and religion separate, personally.