CODA, a coming-of-age drama about the only hearing member of a deaf family, won the Screen Actors Guild’s (SAG) top film award, raising its chances of success at next month’s Oscars ceremony.

The movie follows the story of a small-town girl who pursues her dream of becoming a singer. The film, directed by Sian Heder, cast deaf actors Marlee Matlin and Troy Kotsur as the parents of the young performer, played by Emilia Jones. Kotsur also won the award for male actor in a supporting role.

“We deaf actors have come a long way,” said Matlin through an interpreter...