Race is the correct term. There are generally 5 different noted human races in traditional anthropological studies: Mongoloid (Asian and American Indian), Caucasoid (European), Australoid (Australian and oceanic), Negroid (east African black) and Capoid (south African black).
Thing is, lots of people confuse race with insulting a person. There is lots of questions regarding the 'distinction' of race within the human population. I've often wondered how far off we were from speciation with each other but that takes way too long so it probably was never going to happen with our type of curiosity.
Simplest thing to do is to ask a person if they culturally or ethnically define themselves. Some do, some don't. Some prefer to adopt the country as 'home'. I like to just see people as people.