Is there evidence there was such a tattoo? I'm only familiar with the use of SPQR in inscriptions. I don't even remember seeing it on any coins.

EDIT: I actually own a coin with SPQR on it. I never noticed before. I'm an idiot.

Obviously the Romans didn't use the word tattoo, which comes to us as a result of Captain Cook's voyages through the South Pacific. The word for a Roman tattoo was typically stigma or "mark" which came from the Greek verb "to prick/stick." And tattoos, like brands, were typically reserved for criminals and for punitive purposes.

In the late Empire (VI/V) and Byzantine era, however, the tattoo was used to mark soldiers and military workers, but Commodus reigning in the 2nd century AD is probably too early to have seen it used for anything but punishment. Therefore the marks in the film are probably anachronistic but reflect a later practice.

Vegetius may have been mentioning the practice as that tattooing, since he was a fourth century figure, but again, too late for Gladiator to reflect the practice itself.

Source: Jones, C.P. "Stigma: Tattoo and Branding in Graeco-Roman Antiquity" JRS 77 (1987) pp. 139-55.

Other references to it include:

Cod. Theod. X 22 4: "Brands, that is the national mark, shall be placed upon the arms of the armaments-workers, in imitation of the branding of recruits" (Stigmata, hoc est nota publica, fabricensium brachiis ad imitationem tironum infligatur)

Aetius (527-564): "Stigmates are the marks that are made on the face and other parts of the body. We see such marks on the hands of soldiers. To perform the operation they use ink made according to this formula:

Egyptian pine wood (acacia) and especially the bark, one pound; corroded bronze, two ounces; gall, two ounces; vitriol, one ounce. Mix well and sift.

Grind the corroded bronze with vinegar and mix it with the other ingredients to make a powder. Soak the powder in two parts of water and one part of leek juice and mix thoroughly.

First wash the place to be tattooed with leek juice and then prick in the design with pointed needles until blood is drawn. Then rub in the ink."

http://www.vanishingtattoo.com/tattoo_museum/greek_roman_tattoos.html

It's curious that statues and bas reliefs don't seem to show anything.