Now that Tom Brady's former backup is in the news for being traded to the 49ers ... someone sent us some footage of Jimmy partying during St. Patrick's Day -- and guess what? Bro's gonna bro.

Jimmy G. rolled into the Old Crow Smokehouse bar in Chicago back in March and turned up with his 10 to 15-person bro squad. We're told the QB was like a handsomer, tinier Gronk.

Don't worry ... no Ezekiel Elliott scandal stuff -- just a bro doing bro stuff with his bros.