Menjou was born in Pittsburgh, Pennsylvania to a French father, Albert Menjou, and an Irish mother from Galway, Nora (née Joyce). 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 inThe Blue Envelope Mystery. During World War I, he served as a captain in the ambulance service.
Menjou was married to Verree Teasdale from 1934 until his death in 29 October 1963 and had one adopted son. He was previously married to Kathryn Carver in 1928. They divorced in 1934. A prior marriage to Kathryn Conn Tinsley also ended in divorce.
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, and was later voted the Best Dressed Man in America nine times. His career stalled with the coming of talkies, but in 1930, he starred inMorocco, 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.
In 1948, he published his autobiography, It Took Nine Tailors. Menjou has a star on the Hollywood Walk of Fame at 6822 Hollywood Blvd.
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. Their clashes were reportedly instant, and mutually cutting; Menjou said of Hepburn during the House Committee on Un-American Activities investigation into alleged Communist infiltration, "Scratch a do-gooder, like Hepburn, and they'll yell, 'Pravda'." To this, Hepburn called Menjou, "Wisecracking, witty—a flag-waving superpatriot who invested his American dollars in Canadian bonds and had a thing about Communists." Unsurprisingly, 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 theCBS anthology series The DuPont Show with June Allyson. He also appeared in the Thanksgiving episode of NBC's The Ford Show, Starring Tennessee Ernie Ford, which aired on November 22, 1956. His final film, Disney's Pollyanna (1960) was one his best known roles.
Menjou died on October 29, 1963 of hepatitis in Beverly Hills. He was interred at Hollywood Forever Cemetery.