Cord's first acting role was in the 1961 episode "The Mountain Men" of the TV series Laramie. Cord's second role came a month later as Nino Sanchez in the episode "Winter Quarters" of Frontier Circus. In 1962, he appeared as Larry Rome in the episode "Take a Number" of thecrime drama Cain's Hundred.
Cord appeared in the 1962 film The Chapman Report, directed by George Cukor. He briefly enjoyed a leading man status on the big and small screen during the 1960s and 1970s, and starred or co-starred in mostly crime dramas, action films, and westerns.
In 1963 and 1964, Cord was cast as different characters in five episodes of the series Route 66, including the role of Michael in the two-part "Where There's a Will, There's a Way." In 1964, he played the part of Sam in the episode "If Your Grandmother Had Wheels" of 'East Side/West Side, starring George C. Scott. During this same period, he appeared twice on Naked City, starring Paul Burke.
In 1965, Cord was cast as Jed Colbee in the episode "Survival" of Branded, starring Chuck Connors as a United States Army officer trying to clear his name of a false accusation of cowardice.
In 1966, he played the Ringo Kid, the role originally portrayed by John Wayne in John Ford's 1939 version, in a lavish remake of Stagecoach, which arguably remains Cord's most heavily publicized endeavor.
In 1972, he appeared as Pete Brown in the episode "The Sodbusters" of Gunsmoke. In 1973, he played the role of Haynes in "The Night of the Long Knives" on The F.B.I., starring Efrem Zimbalist, Jr. From 1973 to 1976, he appeared in four episodes of Police Story. In 1979 and 1981, he appeared twice on The Love Boat. In 1988, Cord was cast in an episode of Simon and Simon; in 1988 and 1992, he appeared on Jake and the Fatman. He also appeared in an episode of the War of the World, a TV series. He appeared twice in Murder, She Wrote, starring Angela Lansbury. In 1995, Cord played the character Larry Curtis in the episode "The Guardians" of Walker, Texas Ranger.
Cord is among a handful of actors to appear on both the original and revival versions of CBS's Mission: Impossible. Cord also is known to science fiction enthusiasts for having portrayed Dylan Hunt in the failed 1973 television pilot Genesis II, which was created by Gene Roddenberry. In 1977, he starred as the title character in the epic western Grayeagle.
In 1974, Cord worked twice with Diana Muldaur: as a guest-star on her weekly NBC series Born Free and as her love interest in the motion picture Chosen Survivors, an apocalyptic horror film that acquired a cult status.
Cord now resides in Fort Worth, Texas. Cord suggested that Robert Fuller, his friend from Laramie, also move to Texas to raise horses. Fuller and his second wife Jennifer Savidge did relocate to Cooke County in 2004. Cord and Fuller often make appearances at western film festivals highlighting their continuing mutual interest in "The Spirit of the Cowboy."