Dramatic footage shows the police catching up to the car in Woolloomooloo and striking the driver's window before the thief speeds off.
The owner of the car had arranged to meet the thief, who posed as a prospective buyer, but was pistol-whipped on the head and forced out of the car.
Northern Beaches Superintendent David Darcy said police were "reasonably confident" they knew the identity of the thief. He urged him to hand himself in, saying he was "not going to get away with it".
The man who stole the car is described as Mediterranean or Middle Eastern in appearance with a thin build, possibly aged in his early 20s, with hair that is shaved at the sides and long on the top.
He was wearing a long, black leather jacket, black shirt and pants and white sneakers.