How many Oscars did Out of Africa win?

The African Queen (1951) won one (1) Academy Award (Oscar).

1. Best Actor in a Leading Role - Humphrey Bogart

It was also nominated for the following awards

1. Best Actress in a Leading Role - Katharine Hepburn
2. Best Director - John Huston
3. Best Writing, Screenplay - James Agee and John Huston