At 17, after winning a music talent contest, Davis worked at Theatre Atlanta. He later moved to New York City and attended the American Academy of Dramatic Arts, as well as studied acting at the American Place Theater. After a role on the soap opera How to Survive a Marriage, he performed in off-Broadway plays. In 1976 he was cast as Sally Field's love interest in the television film Sybil. He played the lead role in Larry Kramer's play about AIDS, The Normal Heart (1985). His most successful film role was as the main character in Midnight Express (1978), for which he won the Golden Globe Award for New Star Of The Year - Actor. He also had a small role in Roots.
Diagnosed with AIDS in 1985, Davis kept his condition secret until shortly before his death. Although it was announced he died of AIDS in 1991 in Los Angeles, he actually died of an intentional drug overdose. Near death and in severe pain in a hospital, he opted to return home and end his life on his own terms. With his wife and a family friend present, he committed assisted suicide .
Susan Bluestein Davis continues to campaign to combat AIDS.