The awards were handed out Saturday in Santa Monica.
The drama is written and directed by acclaimed filmmaker Barry Jenkins.
“I cannot even put into words how I feel right now,” King said.
The awards will be handed out next month in Beverly Hills.
Awards will be handed out in New York on Jan. 8.
Oscar winner is already helming Amazon’s “The Underground Railroad.”
The film is based on James Baldwin’s 1974 novel by the same name.