Parker signed to Warner Bros in the late 1930s. He made his debut with an uncredited bit in the Dick Foran Western, The Devil's Saddle Legion (1937). He had small parts in That Certain Woman (1937) with Bette Davis; Back in Circulation (1937) with Pat O'Brien; The Radio Murder Mystery (1937) with Ronald Reagan; Alcatraz Island (1937) with John Litel; Over the Goal (1937) with June Travis; The Adventurous Blonde (1937) with Glenda Farrell; Missing Witness (1937) with Litel; and The Invisible Menace (1938) with Boris Karloff.
Parker's first notable film role was in A Slight Case of Murder (1938) with Edward G. Robinson. He followed it with Accidents Will Happen (1938) with Reagan, but then left the studio.
Parker was married to Marion Pierce from 1939 to 1951. They had one child. They were divorced and Parker married Virginia Field from 1951 until her death in 1992.
Parker decided to go to the stage to learn how to act. He worked for a stock company then tried Broadway, where he had a role in a hit play Johnny Belinda (1940) by Elmer Rice. He then replaced Victor Mature in the cast of the musical Lady in the Dark (1941) opposite Gertrude Lawrence. He went with the show when it toured on the road in 1943. This brought him to the attention of executives at Columbia Pictures who signed him to a long-term contract.
Parker was the second male lead in What a Woman! (1943), a romantic comedy with Rosalind Russell and Brian Aherne.
His career was interrupted by Service with the US Marines. Then when he returned Columbia promoted him to leading man status in the swashbuckler The Fighting Guardsman (1945). Then they starred him in a comedy One Way to Love (1946); and a Western, Renegades (1946).
Universal borrowed him for a support role in You Gotta Stay Happy (1948) with Joan Fontaine and James Stewart. Back at Columbia he supported Don Ameche and Dorothy Lamour in the musical Slightly French (1949). Universal borrowed him for another support part, this time in the Yvonne de Carlo Western Calamity Jane and Sam Bass (1949).
Columbia gave him the lead in some "B"s, Bodyhold (1949), as a Wrestler, with Lola Albright; and David Harding, Counterspy (1950), playing the title role. He played the third lead in the comedy Emergency Wedding (1950), supporting Larry Parks and Barbara Hale.
Parker went to Lippert Pictures to make Bandit Queen (1950), co-starring with Barbara Britton.
Universal used Parker as the third lead in the Western Apache Drums (1951). He had support roles in three films for Pine-Thomas Productions, Caribbean Gold (1952), Sangaree (1953) and The Vanquished (1953). He guest starred on TV in The Adventures of Ellery Queen (1952).
Parker and his wife Virginia Field appeared in "Mr. And Mrs. Trubble" for Schlitz Playhouse (1952). That show invited him back for "Twenty-two Sycamore Road" (1953, with Nancy Reagan), "Little War at San Dede" (1954), and "Visitor in the Night" (1955).
Parker returned to leads with the role of Jesse James in The Great Jesse James Raid (1953) for Lippert Pictures. He had a small role in Kiss Me Kate (1953)at MGM.
He also guest starred on Fireside Theatre in "A Mother's Duty" (1954) and "No Time for Susan" (1955, with his wife), and The Ford Television Theatre in "Kiss and Forget" (1953, with his wife), and "The Mumbys" (1955, with his wife).
Parker was cast as Ranger Jace Pearson in the 52-episode CBS television series, Tales of the Texas Rangers, which aired from 1955 to 1958. His co-star was Harry Lauter as Ranger Clay Morgan. The series was rerun thereafter on ABC.
Parker starred in a low budget Western for Fox, Naked Gun (1956), and Lure of the Swamp (1957). He guest starred in Lee Marvin's NBC crime drama, M Squad (1958) then starred in some low budget Westerns, Lone Texan (1959), Young Jesse James (1960) and Walk Tall (1960). He did "Dr Kate" for Westinghouse Desilu Playhouse (1960). Walk Tall was directed by Maury Dexter who used Parker in The High Powered Rifle (1961) andAir Patrol (1962).
He guest starred in ABC's religion drama series, Going My Way, starring Gene Kelly and Leo G. Carroll as Roman Catholic Priests in New York City. Parker was cast as Msgr. Joe Giblin in the 1962 episode, "The Crooked Angel."
He had the lead in the British film The Earth Dies Screaming (1964) and was one of many names in Waco (1966).
His last film role was in The Great Waltz (1972).
