Patrick Anthony McGurk is accused of aggravated vehicle taking and dangerous driving over the crash in west Belfast on Sunday.
The 25-year-old, of Albert Street in the city, is also charged with four counts of assault on police.
He was arrested close to his home in the lower Falls area following the collision involving a Renault Mégane.
A 17-year-old boy was also detained but released on police bail pending further enquiries.
The vehicle had been reported stolen from the east of the city on Saturday night.
McGurk made no bail application during an appearance before Belfast Magistrates' Court.
His lawyer did not put any questions to the police officer who connected him to the charges.
District Judge Fiona Bagnall remanded him in custody to appear again by video link on 15 March.
Meanwhile, footage has emerged on YouTube, referring to the Divis Hoods and showing a blue Renault Mégane being driven erratically.
A number of youths are shown whistling to alert those inside the vehicle when an unmarked police car approaches. A patrol car also arrives, hemming in the stolen car.
Both missiles and verbal abuse are hurled at arresting officers by onlookers.
No one was injured.