Not really. People love to quote Leviticus 19:28 which says:
Do not cut your bodies for the dead or put tattoo marks on yourselves. I am the LORD.
But this prohibition was centered around forbidding the Israelites to mimic the practices of their pagan neighbors. Since modern tattoos are not connected with pagan worship practices it really doesn’t transfer.
I think the best consideration for either getting or not getting a tattoo is 1 Corinthians 6:19-20 which says:
Do you not know that your body is a temple of the Holy Spirit, who is in you, whom you have received from God? You are not your own; you were bought at a price. Therefore honor God with your body.
The first consideration every Christian ought to make concerning a tattoo is whether the Lord has given the go ahead. According to the passage above, your body no longer belongs to you. It’s His—bought and paid for by His blood—so you need to make sure He’s okay with it.
Secondly, any consideration for a tattoo needs to be in keeping with the exhortation to “…honor God with your body.” Is the tattoo something that will bring honor to the Lord?
Finally, Christians are to be influenced by the Word—NOT the World! If the motivating factor for getting a tattoo is simply because they’re popular then you might want to reconsider your decision. As a believer, you are to be led by the Spirit of Christ, not the spirit of the world.