Mobile police said the warrant was issued Thursday and signed by Cousins' ex-girlfriend, Christy West. He could face a third-degree domestic violence charge of harassing communications.
West, the mother of Cousins' 7-year-old son, filed a police report Aug. 23, according to USA Today Sports. The report was filed two hours after an alleged phone call from Cousins in which he threatened her.
West recorded the phone conversation with Cousins, who threatened to shoot her in the head over allowing their son to attend the NBA player's wedding to another woman. TMZ Sports released the footage Tuesday.
Cousins' ex-girlfriend also accused him of previously choking her and is seeking a restraining order, according to court documents.
Cousins, 29, signed a one-year deal worth $3 million with the Lakers this summer. He is expected to miss the entire season after suffering a torn ACL two weeks ago in a pick-up game.
The NBA and Lakers each issued statements earlier in the week that they are investigating the incident.