The motorcyclist, a 35-year-old man from York, suffered injuries to his ribs, pelvis and arm in the collision which occurred on the A59 at the junction with Station Road at Goldsborough, at around 6am on Wednesday 19 February 2014.
He was taken to Leeds General Infirmary for treatment to his injuries, which are not believed to be life-threatening.
He sustained his injuries when his orange motorbike, which was travelling towards Knaresborough, collided with a white Vauxhall Corsa. The driver of the car, a 50-year-old local woman, was badly shaken by the incident but was otherwise uninjured.
Officers are appealing for any witnesses to come forward, in particular anyone who witnessed the collision or saw either vehicle prior to the incident.
Please quote reference number 12140027210 when passing information about this incident.