According to new legal docs ... the rapper's been ordered to fork over $135,777.11 to Jessica Brown for damages after she sued him for defamation and invasion of privacy. It was a default judgment ... meaning the judge sided with Brown because Desiigner didn't contest it.

We broke the story ... Brown filed suit against Desiigner in February 2018, months after he shared an Instagram post referring to her as a "fraud," and warning his followers to stay away from her and her "college scams."

Jessica, president of a company called College Gurl, claimed she educates young people on how to pay for college and helped Desiigner's sister, Siera Shelby, get into Howard University.

Shelby later left school and left some belongings behind, and Desiigner allegedly believed it was all a con job ... and went off on Brown on social media.

We reached out to him ... no word back so far.