CHRIS Brown surrendered his phone at the Rehab

Chris Brown surrendered his phone and the Internet while in rehab for anger management, TMZ has learned -- but he didn't give up his weed without a fight.

When Chris enrolled in his court-ordered rehab joint after last week's progress hearing in the Rihanna beating case ... he asked the rehab staff if he could bring his weed along.

Chris told staff the Mary Jane was prescribed by a doctor for a medical condition -- depression --  but the staff rejected his request. We're told Chris kicked up a stink, claiming pot makes him calm, but the staff was unbending.

As we reported, the judge in the case ordered Brown to enroll in a live-in anger management facility for 90 days following his previous stint in anger rehab, when he was booted after just two weeks ... ironically because he flew into a violent rage.

Hopefully the no-weed rule won't exacerbate Chris's anger problems. They won't like him when he's angry.