1:20 PM PT -- A police spokesperson tells TMZ Sports, "No arrest has been made yet. Hopefully, he will turn himself in on the active misdemeanor arrest warrant."
An arrest warrant has been issued in Alabama for DeMarcus Cousins stemming from a threatening phone call he allegedly made to the mother of his child, cops say.
"An arrest warrant has been issued," a spokesperson for the Mobile Police Dept. told USA Today.
According to the MPD's website, Cousins is facing a domestic violence charge -- 3rd-degree harassing communications, a misdemeanor.
The charge carries a maximum sentence of 1 year behind bars.
TMZ Sports broke the story ... the NBA star's ex-girlfriend, Cristy West, told police she recorded a phone call with Cousins in which he threatened to "put a bullet in your f*cking head" if she wouldn't let their 7-year-old child attend his wedding.
West lives in Alabama and the wedding took place in Atlanta.
During the call, West told Cousins she would NOT allow the child to attend -- though she did not explain why.
In court docs filed by West, she claims Cousins had choked her during a previous incident -- but she did not elaborate.
As for Cousins, the Los Angeles Lakers star -- who suffered an ACL tear earlier this month -- has not commented on the allegations.