Reincarnation is the teaching that a person's soul, after death, goes to a holding place and after a while enters a new human body. This cycle continues over and over again for thousands of years until the person learns what needs to be learned, and then the reincarnation process ceases.
A Christian who believes the Bible should not believe in reincarnation. The Bible tells us in Hebrews 9:27 that it is appointed to men to die once, after this comes judgment. Reincarnation would contradict this teaching. Therefore, reincarnation is not true, and the Christian should not believe in it.