Her career began in 1921, and Moran appeared in a couple of silent movies in the early 1920s. She is probably best known for her role, as Laurel Dallas, daughter of the title role in the 1925 film Stella Dallas. She appeared in early sound movies such as Behind That Curtain (1929), and some musical movies, such as A Song of Kentucky (1929), Words and Music (1929), and Mammy (1930). She then moved to Broadway, where she appeared in the straight play, "This is New York" (1930), and the musicals, "Of Thee I Sing" (1933) and "Let 'Em Eat Cake" (1934).
She also had a brief affair with writer F. Scott Fitzgerald while he was married to Zelda Fitzgerald. He once remarked that she was "The most beautiful girl in Hollywood". She was also an inspiration for the character of Rosemary Hoyt in Fitzgerald's novel Tender is the Night (1934).
In 1935, she married Clarence M. Young, Assistant Secretary of Commerce, temporarily retiring from her acting career. They had one son, Timothy.
Moran also had a co-starring role in the short-lived TV show Waterfront (1954–1955). The show starred Preston Foster as Capt. John Herrick, and Moran as his wife May Herrick.