While we can’t absolutely say it’s not safe, most doctors don’t recommend it.
First, there’s the risk of a blood-borne infection like hepatitis B, hepatitis C or HIV due to improper equipment sterilization. Any infection you contract could be passed on to baby.
Even if you feel sure you’ve found a safe tattoo parlor, there’s a big unknown factor. Very little is known about the effect tattoo dyes and inks can have on a fetus, so it’s probably better to err on the side of caution. Lower back tattoos can also be a problem if you plan to have an epidural. Again, while there’s no clear evidence that supports or condemns giving epidurals near tattoos, many doctors employ the “better safe than sorry” theory here. Definitely check with your own OB before getting inked in that area.
Finally, there’s the cosmetic factor—remember, your skin changes during pregnancy. A tattoo you get during month three of pregnancy will more likely than not look quite a bit different when baby is 3 months old.