Some religious texts, including the Bible, ban divination as a whole. However, the exact interpretation of "divination" varies considerably among believers. Some Christians today believe all forms of divination are contrary to God, either because knowledge of the future is only known to God (thus making diviners both arrogant and fraudulent) or because the ability for mortals to divine must come from the Devil.
However, in previous centuries, certain forms of divination were highly popular and accepted in Christian Europe. Astrologers were common figures in royal courts, and even some popes consulted them. A distinction was made between attempts to predict the future, which was considered heretical, and attempts to gauge the influences that will be in play at any particular moment without making any guarantees as to ultimate outcomes. This logic can be extended to tarot reading and many other forms of divination as well.
The historical reality is that most tarot readers have been Christians. Whether it is proper behavior for a Christian (or any other religious group) is ultimately a personal spiritual decision.