Police said the victim aged in his sixties was sat in his red Nissan Qashqai in Elsworth Terrace at Armley at 7am on New Year's Day when a man opened the door and pulled him out of the car.
The suspect then drove off in the car, which was later found with fire damage at the rear of Ley Lane.
The victim suffered slash wounds to both his hands in the incident and required hospital treatment.
The suspect is described as an Asian male, possibly in his thirties.
He was of skinny build, around 5ft 7in tall and was wearing a grey zip-up hooded top.
Anyone who witnessed the incident or the vehicle - which has the registration number YG67 MMA - being set alight is asked to contact the Leeds District Crime Team on 101 quoting crime reference number 13180000563.
Information can also be given anonymously to the independent charity Crimestoppers on 0800 555111.