It really depends on your POV of the scripture.
1. If you do not believe in following the Torah, then no it would not be a sin based off of that POV.
2. a) If you do believe in following Torah you could go off the fact that it states in context not to mark/tattoo your body for someone who dies. So if you take literal context, getting a tattoo that is like a bible verse or an animal or something non-death related, then no I would believe it not be a sin.
2. b) Or if you're someone who follows Torah, and you look at the whole context of the chapter it is in. Leviticus 19 as a whole starts off stating:
Leviticus 19:1-2
"Adonai said to Moshe, [SUP]2 [/SUP]“Speak to the entire community of Isra’el; tell them, ‘You people are to be holy because I, Adonai your God, am holy."
Again if you follow Torah, and look at in this aspect God is calling His people to be a holy nation (not do as other nations do), and if you look at the whole context and not just the verse of being holy, then I would say that getting a mark/tattoo on the body would be sin.
So really it comes down to what your convictions are as far as how you follow scripture.