Most people quote the verse from 1 Cor to cover a "No" answer on this one.
The verse in 1 Corinthians. covers sexual immorality in the church as a whole, not about the individual. How is that meant to link to tattoos being placed on the body??.. perhaps i shouldn't drink coffee or eat from Mcdonalds because caffeine and trans-fats is poisonous and addictive, and im putting it in my body. let's reference it to Corinthians! (not that addiction can't be referenced in the bible, but you get my point)
You can't just take a verse and make it mean what you want it to mean.. it's dangerous, and intentially or not, in a worse case scenario, it can create gospels within Gospel.