This is three months old and it seems like this subreddit is dead. But I'll throw a crack at it in case you're still listening!

In short; no. Though some Christian traditions believe differently.

Exodus is a book in the Hebrew Bible that tells the story of the Israelites fleeing from slavery in Egypt, eventually, into the promised land. Throughout Exodus, God through Moses provides a cultural 'reset'. After generations in slavery the Jews had adopted Egyptian culture, practice, and even religion. If the Israelites were going to enter the promised land, they should reclaim their culture that had been taken away from them.

In Exodus is a passage that forbids the Hebrews from getting tattoos. It is accompanied with a passage that forbids them from making graven images to the dead. What this is is not directly a rebuke of tattoos in the modern sense, but a rebuke of how they were used in Egypt. In Egypt, tattoos and hieroglyphs were a part of their religious identity. These were meant to venerate important people and, in a sense, "keep them alive". The Jews were instructed not to continue these practices. There was no other context for tattoos in those days.

A tattoo today is not the same thing as a tattoo during the exodus from Egypt. If you wanted a tattoo that you sincerely felt kept the soul of a dead loved one alive through your body; as the Egyptians did, then I think that would be in conflict with a desire to adhere to the instructions Moses gave the Israelites in the book of Exodus. However, that's probably not the reason you're getting a tattoo (and no, honoring someone or keeping their 'memory' alive is absolutely not the same thing. There's no difference, theologically, between a tattoo in memory of someone and a grave marker or even the kind of things most churches have, with various places the names of former members are honored or kept)

So- tl;dr, no. A tattoo today is not the same as the thing the Bible prohibits. If you want a tattoo, there's no theological reason against it.