There is at least a huge quantity of Roman “bathroom graffiti”. In order to make them appear more serious, they are generally called “epigraphy”, and they are one of our very best sources about Roman society in general.
Not sure how far back it goes, but I would not be surprised if the oldest extant text were a bathroom graffito.
In his book "Una giornata nell'antica Roma" (I don't know if an English translation is avaible) Alberto Angela describes the daily life of Rome's citezens during the reign of Trajan (roughly set in 115 A.D.).
In the chapter describing the insulae, the typical house of the lower classes, he also describes some of the drawings found on their walls, comparing them to bathroom graffiti. For example, he describes
a drawing, probably made by a kid, of two gladiators fighting
a graffiti that says "Restitutus multas decepit saepe puellas", a warning written probably by a woman that says "Restitutus has often deceived lots of women"
A declaration of love "Marcus amat Domitiam"
A prostitute ad "Eutychis / Graeca assibus II, / moribus bellis " that translates in "Eutychis, greek, of fine manners, offers herself for two "assibus" (Roman currency)
These are just a few examples, as CubicZircon said, there are lots of Roman "graffiti".