New police video, obtained by TMZ Sports, shows Marcus Jordan name-dropped his famous father to cops in an apparent effort to get out of trouble before his arrest on Tuesday morning.

The footage was captured on Maitland Police Department officers' body cameras at 1:14 AM ... right around the time cops first discovered Marcus and a woman inside a blue Lamborghini SUV that had gotten stuck on some train tracks.

Initially, you can see in the video that Jordan tried to move the car off the railway with his foot on the gas ... but when the pricey ride's tires spun in place no matter how hard he pressed, cops asked him to get out of the vehicle.

Jordan tried to get the police over and over again to help him break his car free ... but as he was eliciting signs of being intoxicated (his speech seemed slurred and his balance appeared off) -- cops made it clear they weren't going to assist in that task.

Instead, they asked to pat him down ... and when they felt along his waistband -- he brought up his NBA legend father.

"Bro," he told one of the officers. "I'm Marcus Jordan. I'm Michael Jordan's son. I'm not doing anything wrong. I'm just trying to get home. And I made a wrong turn. OK?"

"And," he continued, "clearly, we would just like to get our car off of the f***ing train tracks which we were not trying to be on."

Cops eventually walked Jordan away from his car -- which he said cost $300,000 -- and after he admitted to having a night out on the town with some beverages prior to getting behind the wheel ... they administered some field sobriety tests.

After cops felt he failed the tests ... they put him in cuffs and told him, "I believe you've had too much to drink tonight." Marcus said he "disagreed with that."

Seconds later, cops can be seen in the video searching Marcus' person ... and as they dug around one of his pockets, they pulled out a small baggie full of a white powdery substance that they later claimed in police documents tested positive for cocaine.

Marcus clearly grew agitated during the search ... at one point he could be heard telling the officers all they'd find in his pants were a "big dick and some big balls."

As they tried to put him in the back of a patrol car moments later, Jordan did not want to get in -- and demanded they "chill the f*** out." Eventually, he got in -- and was transported to a nearby jail.

On the way, though, Marcus quarreled with an officer over his level of fame. He also intermittently sang along with the cops' radio.

Marcus was ultimately booked on three charges -- DUI crash with property damage, possession of cocaine and resisting an officer without violence -- and he was released from custody a few hours later.