The New Testament of the Bible does not comment on whether or not believers are allowed to get tattoos. However, a passage from Leviticus 19:28 in the Old Testament states that one should avoid cutting themselves or marking the skin with tattoos, which could indicate that tattoos are sinful.
The Bible states that it is best not to engage in an activity if there is any doubt about whether or not it would please God. A passage from 1 Corinthians 6:19-20 declares that each person's body is a temple of the Holy Ghost, and that everyone should honor God with their bodies. Thus, tattoos may violate God's wishes.