Cox, who also releases solo material as Atlas Sound, will portray the lover of Jared Leto's character in the movie, according to The Hollywood Reporter.
Griffin Dunne (After Hours, House of Lies) and Denis O'Hare (True Blood, Milk) have also been cast as doctors.
The Dallas Buyers Club stars Matthew McConaughey as Ron Woodruff, who was told he would only live for six months after developing Aids in 1986, but survived for six years.
Based on a true story, Jean-Marc Vallée's movie tells how Woodruff set up a smuggling operation to make alternative medicines available to Aids patients, after he becomes frustrated with the lack of healthcare options available to him.
McConaughey recently made headlines as a result of the dramatic weight loss he has undergone to play Woodruff.
Leto has been cast as an HIV-positive man who meets Woodruff in hospital.
Shooting on The Dallas Buyers Club is to take place in New Orleans.