You highlighted your answer already: nota would indicate the physical tattoo in that sentence of Cicero's. We see it used in Pomponius Mela, too:
Mossyni...notis corpus omne persignant
The Mossyni "sign" their whole body with notes (words?).
You'll should keep the perfect passive participles with it, though, if you plan on using it to describe someone.
There are a few other words for tattooing, besides compungere. Mela also uses pingere:
Agathyrsi ora artusque pingunt
The Agathyrsi paint their faces and limbs.
I don't know if we know whether this was literal painting, but Lewis and Short use tattoo here.
You also have this passage from Pliny the Elder (22.1.2):
inlinunt certe aliis aliae faciem in populis barbarorum feminae; maresque etiam apud Dacos et Sarmatas corpora sua inscribunt.
That, among some barbarous peoples, the females stain the face by means of various plants, there can be little doubt, and among the Dacians and the Sarmatians we find the men even marking their bodies.
inlinere here probably does not indicate needle under the skin tattooing, but something like how henna is used in India. Similarly, there's just no way of knowing if the Dacians and Samartians used needles or marked their bodies some other way.
If you go even later, Isidore uses stigma, -atis as a tattoo, which is a borrowing from the Greek στίγμα. This usage goes all the way back to Herodotus, but you see it in a variety of locations
στίγμα, ατος, τό, tattoo-mark, Hdt.5.35, Arist.HA585b33, GA721b32, IG42(1).121.48, al. (Epid., iv B.C.), Polyaen.1.24; στίγμα ἱρά, showing that the persons so marked were devoted to the service of the temple, Hdt. 2.113; esp. of a slave, Pl.Com.187, Ps.-Phoc.225, Cod.Theod.10. 22.4; or a soldier, ibid., Aët.8.12; “στίγματα ἐξαίρει βατράχειον καταπλασθέν” Dsc.Eup. 1.110