No you cannot determine a persons race with dna. Example if I wanted to know if I was of african descent or indian descent just by doing a dna test would not tell me this, but if I wanted to know if a man who is Indian or african was my father then I could have a dna sample of his tested against mine and that would tell me if I was related to him that in turn would allow me to determine that I was part Indian or African. There is not a gene that determines race.
