I have to admit I had a chuckle at the linked image when I realized what it was talking about.

The 'Romans' being mentioned in the thing aren't historical Romans. This is referring to a practice in a fictional children's book series (Rick Riordan's Heroes of Olympus). The characters in the Roman god camp (as opposed to the Greek god camp) get a tattoo exactly as pictured. A symbol representing their godly parent, SPQR, and then a bar for each year at the camp.

I imagine the image was originally created for a Percy Jackson/Heroes of Olympus group, and has since spread.

Regardless, it's not historical at all, and it would be impossible to find records of the practice, as it's entirely made up by the author.