Born in London in 1898, Rapper emigrated to the United States and became an actor and stage director on Broadway while studying at New York University. In 1936, he journeyed westward to Hollywood, where he was hired by Warner Bros. as an assistant director and dialogue coach. He proved invaluable in translating and mediating for non-native English-speaking directors. By the early 1940s, he had metamorphosed into the one of the hottest directors on the Warner Bros. lot.
He made his directing debut with the 1941 film Shining Victory, in which his friend, Bette Davis, appeared as a show of support for him. He would go on to direct her in four more films: Now, Voyager (1942), The Corn Is Green (1945), Deception (1946), and Another Man's Poison (1952). Rapper's film, One Foot in Heaven (1941), earned an Oscar nomination for best film. He worked with such performers as Fredric March, Kirk Douglas, Eve Arden, Claude Rains, and Ronald Reagan.
Near the end of his directorial career, Rapper made two more films for Warner Bros., Marjorie Morningstar (1958), based on Herman Wouk's novel, and The Miracle, a 1959 remake of the 1912 Austrian film Das Mirakel. Both versions of The Miracle were based on the famous stage pantomime by Karl Vollmöller and Max Reinhardt.
Other biopics directed by Rapper include The Adventures of Mark Twain (1944), Pontius Pilate (1962) and his last film, the 1978 flop Born Again, about convicted Watergate conspirator and former Richard Nixon aide Charles Colson.