According to the police report, obtained by TMZ, cops were called to the "Black Beatles" rapper's Doral, FL home on January 22 for a domestic disturbance ... and that's when Slim told them Kiara Danielson hit him.

Officers say Slim told them the dispute started with an argument over social media, with Slim trying to get Kiara to leave his place ... but things allegedly spiraled from there.

Slim told cops he threw Kiara's belongings into the yard, and that's when she got aggressive ... punching him in the face 3 times.

Kiara's telling a different story, though -- police say she claimed she whipped out her phone to record Slim during the dispute and he reached for it ... they struggled and she scratched his eye.

Cops also say she told them Slim grabbed her at one point during the fight.

The officers say Slim had a scratch on his eye, and Kiara had no visible injuries ... so they deemed her the primary aggressor, and arrested her for domestic violence.

She was hauled off to jail and booked for misdemeanor battery.

The incident went down the day after the couple had another explosive fight ... this one while at her Miami apartment.

We obtained video of that argument, showing Slim taking his belongings from her place -- so, maybe not all that shocking things boiled over 24 hours later.

It's interesting, the domestic violence arrest comes about 2 years after Slim was arrested for battery ... when he allegedly attacked Kiara during a fight that started over ... once again, social media.