I don't think you can get the tattoo transferred unfortunately.

It is like this due to lore because basically if your character was in 1.0 it was marked by the calamity. So any characters made in 2.0+ technically didn't go through the calamity and therefore no tattoo.

It would be nice I guess if you had a legacy status account and at least one character with the tattoo that your other newer made characters could also have the tattoo...I mean you could try requesting that SE do that I guess, but besides that like I said above I think it is due to lore so they may not want to do that.

In the end...you barely ever see that tattoo. My main has it, but I rarely ever see it due to gear covering it. So I would suggest just not worrying about it since it isn't something you'll see much even if you had it.