Menjou was born in Pittsburgh, Pennsylvania to a French father and an Irish mother from Galway. He was raised Catholic and attended the Culver Military Academy, graduating from Cornell University with a degree in engineering. Attracted to the vaudeville stage, he made his movie debut in 1916 in The Blue Envelope Mystery. During World War I, he served as a captain in the ambulance service.
Returning from the war, he became a star in such films as The Sheik and The Three Musketeers. When he starred in 1923's A Woman of Paris, he solidified the image of a well-dressed man-about-town. Menjou was famous for wearing fine clothing in many of his films. His career stalled with the coming of talkies, but in 1930, he starred in Morocco, with Marlene Dietrich. He was nominated for an Academy Award for The Front Page (1931).
In 1947, Menjou cooperated with the House Committee on Un-American Activities in its hunt for Communists in Hollywood. Menjou was a leading member of the Motion Picture Alliance for the Preservation of American Ideals, a group formed to oppose Communist influence in Hollywood. Other members included John Wayne, Barbara Stanwyck (with whom he co-starred in Forbidden in 1932 and Golden Boy in 1939) and her husband, actor Robert Taylor.
Because of his political sympathies, Menjou came into conflict with actress Katharine Hepburn. Menjou appeared with her in the films Stage Door and State of the Union, which also starred Spencer Tracy. Hepburn was strongly opposed to Americans co-operating with the McCarthy hearings. It was reported by William Mann in his biography of Hepburn, Kate, that during the filming of State of the Union, she and Menjou only spoke to each other when required to in the film script.
Menjou ended his film career with such roles as French General George Broulard in 1957's Paths of Glory, and as the town curmudgeon in Pollyanna in 1960.
He guest starred as Fitch, with Orson Bean and Sue Randall as John and Ellen Monroe, in an 1961 episode, "The Secret Life of James Thurber," based on the works of the American humorist James Thurber, of the CBS anthology series The DuPont Show with June Allyson.
In 1948, he published his autobiography, It Took Nine Tailors. He died on October 29, 1963 of hepatitis. He is interred at Hollywood Forever Cemetery.
Menjou has a star on the Hollywood Walk of Fame at 6822 Hollywood Blvd.