Is Trump racist?

[Lyin' Steve]

No.  It's a cheap, effortless slur that people on the left who hate Trump use to shame and intimidate anyone who dares to not jump on the Trump-hating bandwagon.

Trump has never advocated any policies that discriminate against people because of their race, nor has he ever made discriminatory or bigoted remarks about people because of their race.  What he has done is thrown Black Lives Matter protesters out of his rallies and advocated for sending illegal Mexican immigrants back to Mexico.  This policy is motivated by an aversion to a particular country, not to a particular race.  Probably the closest he's gotten is "we speak English here, god damn it, don't speak Spanish at your rallies Jeb!" but this is coming from a place of nationalism rather than racism, and Hillary herself in 2008 said English was the national language (although she awkwardly opposed making it official).

[Lyin' Steve]

His anti-Muslim policies are probably as bigoted as he gets, but like Wilhelm said, Islam is a religion, not a race.
Plus it's pretty apparent that he is just saying stuff like that to get to the right of the field on national security.  He wasn't advocating for any such policies until after San Bernardino.