Jamie Lee Sharp, 25, took the keys during a house raid in Gloucester along with James Honeywell, 26.
In the video he is seen revving the engine and boasting to friends on the phone about "his new car".
At Gloucester Crown Court, Sharp, of Gloucester, was jailed for four years and disqualified from driving.
Honeywell was jailed for 35 months.
The pair had broken into a house in the Longlevens area of Gloucester on  11 January and along with the car keys, stole a television, a wallet and several other items, the court heard.
After leaving, Sharp filmed himself just before he crashed into a wall in nearby Barnwood Road.
In the aftermath, Honeywell ran off leaving Sharp trapped.
Sharp, previously of Deans Way, Gloucester, pleaded guilty to burglary, aggravated vehicle taking, driving whilst disqualified, drink-driving and driving without insurance.
He was jailed for four years and disqualified from driving for 29 months, in June.
Honeywell, of Elmleaze, Longlevens, Gloucester, was jailed on Monday for 35 months after admitting burglary and aggravated vehicle taking.
He had failed to attend court on 19 November for sentencing and a warrant for his arrest was issued.
A burglar who stole a Porsche and filmed himself boasting behind the wheel before crashing it into a wall has been jailed.