Yes. In fact, most of the United States's history of immigration is one of racial selectivity. For years there was a racial quota system of how many people of specific nationalities could enter the United States. The most stark example of this is the Chinese Exclusion Act, enacted in 1882 but consistently renewed until the early 20th century when it was made permanent. This policy was not repealed until the early 40s, and the racial quota system still remained in effect until the 1960s.

So, yes, the United States has absolutely discriminated and have sought to impose limits on which specific nationalities should enter the country.