It's hard to say, Romans themselves were of mixed stock. According to traditional sources when the city was founded they welcomed people who had no home themselves: outcasts, exiles, criminals, anybody. Julius Caesar would be considered caucasian, but his ethnicity identity had nothing to do with race, he was Roman. A Black African from North Africa who lived in Roman jurisprudence and was a citizen was Roman. Originally Romans were what I would say is caucasian, but that term is very broad and doesn't really account for nuanced ethnic identity.
There are cases though where leaders like Hadria, Trajan and Theodosius were all born in the province of Hispania, in Spain. They likely had celtic and Iberian ancestors, but they were Roman.
That is, if I understand the concept of Roman ethnicity correctly. There were 'others' in the Empire who were not seen to be Roman, but Romanized... the Britons and Germans for example.