NO. There was no concept of "race", as understood by us now, in Ancient Rome.Let's say that historically Romans became almost really racist [in the modern sense]
Let's be clear, most modern scientists do not accept that races (within humanity) actually exist. The idea of racial groups is a human concept. This idea arose only a few centuries ago.
The Romans did not have the concept of race. They certainly had the concepts of heiracrchies of humans, free-born and slaves, Roman citizens and non-Roman citizens, humiliores and honestiores, city dwellers and rustics, men and wome friend and foe. Such categorisations made ample opportunity for discrimination and boundless cruelty, which were exercised with great viciousness. But they were not racist.