The prize, announced Monday, will be presented at the guild's awards show Jan. 24.
"Milk" stars Penn as San Francisco politician Harvey Milk, who in 1977 won a seat on the board of supervisors to become the first openly gay man elected to major public office in the United States. The film is directed by Gus Van Sant.
The following year, Milk was slain along with Mayor George Moscone by a board colleague.
The Kramer Award is named after the legendary filmmaker whose works include "The Defiant Ones,""Judgment at Nuremberg" and "Guess Who's Coming to Dinner."
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