The crash happened in the Bracken Hill area at around 1.30pm yesterday after officers from the Roads Policing Group tried to pull over the green Toyota Avensis.
It is alleged the driver then tried to get away, causing minor damage to a patrol car in the process.
The driver, a 22-year-old local man, was arrested at the scene.
A North Yorkshire Police spokesman said: "Following questioning, he was remanded in custody after being charged with six offences - driving without due care and attention, driving without a licence, driving while disqualified, driving without proper control of the vehicle, driving without insurance and failing to stop for the police.
"He is due to appear at Scarborough Magistrates’ Court today."