The only verse in the bible that actually makes mention of tattoos being a sin is Leviticus 19:28 where the word of God says:
You shall not make any cuttings in your flesh for the dead, nor tattoo any marks on you: I am the Lord.
Although many people use this as an argument against tattoos, I personally do not. That is because in the verses before and after this one there are some laws given which we break today all the time! For example verse 27 says:
You shall not shave around the sides of your head, nor shall you disfigure the edges of your beard.
Now we all know men, even preachers, who do this. Are they sinning every time they get a haircut?
This chapter in Leviticus also says we are supposed to observe the Sabbath. Christians don't do that nowadays. Unless we agree that men shouldn't shave or that we must honor the Sabbath, etc. it is hypocritical to use Leviticus 19:28 as a means of telling people not to get tattoos.
However, this is what I always tell people when they ask me if getting a tattoo is a sin (especially people who go to church). It is always going to be hard for tattoos to be accepted in church for cultural reasons. In time past, tattoos were most widely recognized as being associated with Ancient Egyptian, Ancient Greek, culture (etc.). All of which had religious beliefs and ceremonial practices that were not Christian.
Tattoos got introduced to Anglo-Saxon culture when American settlers came in contact with the culture of Native Americans. Once again, their religion was different from the Christian religion. So you can see how getting tattoos could easily have been something that passed down through Christian generations as an act of going against your own religion (and into someone else's). So even if you wanted a tattoo for innocent reasons, this is why people with traditional Christian values always saw it as being wrong.
Here's the bible scripture(s) I always tell to people who want tattoos (or who want to engage in anything that they think is not that big of a deal while others think its a sin). Paul says in 1 Corinthians 8:
9 Be careful, however, that the exercise of your rights does not become a stumbling block to the weak. 10 For if someone with a weak conscience sees you, with all your knowledge, eating in an idol’s temple, won’t that person be emboldened to eat what is sacrificed to idols? 11 So this weak brother or sister, for whom Christ died, is destroyed by your knowledge. 12 When you sin against them in this way and wound their weak conscience, you sin against Christ. 13 Therefore, if what I eat causes my brother or sister to fall into sin, I will never eat meat again, so that I will not cause them to fall.
Here Paul is saying, it is not a sin to eat meat even though many people believe so due to the old laws given in the Old Testament. However, he says a Christian who is new to the faith might not understand how and why it is not a sin. Whereby, he will follow you in eating meat, but will have a guilty conscience about it, while your conscience is free. See, Paul explains in Romans 14:23 that whoever eats meat with a guilty conscience is actually sinning because they believe it is a sin yet choose to do it anyway. He says:
But whoever has doubts is condemned if they eat, because their eating is not from faith; and everything that does not come from faith is sin.
So even if your conscience is free because you know eating meat or getting a tattoo or working on the Sabbath or not shaving are Old Testament laws for when people were under the law, a person who does not know that will follow you. However, because they are following you thinking they are doing something wrong, their own decision to do what they think is wrong is an act of "sin" according to the bible; even if it is not really wrong! The rebelliousness against their own guilty conscience is what is judged as wrong.
So Paul puts it best in Romans 14:19-22 when he says this:
19 Let us therefore make every effort to do what leads to peace and to mutual edification. 20 Do not destroy the work of God for the sake of food. All food is clean, but it is wrong for a person to eat anything that causes someone else to stumble. 21 It is better not to eat meat or drink wine or to do anything else that will cause your brother or sister to fall.
22 So whatever you believe about these things keep between yourself and God. Blessed is the one who does not condemn himself by what he approves.
Food for thought :-)