Alcohol has been around forever and in almost every culture. A Roman could have been addicted to alcohol.

Meth, MDMA, LSD, and DMT are synthetic drugs that Romans would not know how to produce.

Cocaine is extracted from Coca plants. I doubt Romans had access to coca plants as they are native to South America, but even if he did he wouldn't have the techniques to extract enough cocaine to get high.

Heroin is in a similar position to cocaine. It is plant based but requires advanced chemistry to extract opium from a plant then convert it into heroin.

Romans had access to opium, but I don't know if the supply was large enough for people to become addicted to it. Opium addiction was possible, but I don't know how often it occurred.

Tobacco is native to the Americas so a Roman would not have access to it.