The Council of Conservative Citizens has released a statement through their website objecting to Elba playing Norse god Heimdall in the comic book movie.
"It’s not enough that Marvel attacks conservatives values, now mythological Gods must be re-invented with black skin," a post on the site reads.
"It seems that Marvel Studios believes that white people should have nothing that is unique to themselves. An upcoming movie, based on the comic book Thor, will give the Aesir an insulting multicultural makeover. One of the Gods will be played by Hip Hop DJ Elba."
The post ends by linking to a 'Boycott Thor' website.Speaking about his casting earlier in the year, Elba said: "Thor has a hammer that flies to him when he clicks his fingers. That's okay, but the colour of my skin is wrong?"
Thor is due out in cinemas next May.