The Mobile municipal court website lists a third-degree harassing communications charge against Cousins, but no other details have been disclosed. A police spokesperson told USA Today Sports that "an arrest warrant has been issued."
Christy West, a former girlfriend of Cousins', is seeking a restraining order against him after she said in court documents and in a police report obtained by TMZ that he threatened her and has previously choked her.
West, according to TMZ, alleged that Cousins said he would put a "bullet in (her) f---ing head" during an argument over allowing their 7-year-old son to attend Cousins' wedding to another woman.
The NBA and Lakers on Tuesday said in statements that they were "investigating the allegations."
Cousins has declined to comment.
TMZ shared an audio recording West took of the incident, and she said that the male voice heard is that of Cousins.
During the argument, the man says, "I'm gonna ask you this one more time before I take it to another level ... Can I have my son here, please?"
After West responds "No," the man makes the threat and the audio clip ends.
Cousins got married in Atlanta on Saturday, and his son was not there, according to TMZ.
The 29-year-old former All-Star suffered a torn ACL earlier this month and could miss the entire season -- his first with the Lakers.