The pursuit started near Bolton Abbey on Sunday afternoon when officers came across suspected quad bike thieves, who drove off crossing onto the wrong side of the road.
Officers had been called earlier in the afternoon about two suspects disturbed while trying to steal a quad bike in Starbotton.
The chase weaved all the way towards Addingham, where officers had deployed an extra stinger to corner the two suspects.
One of the motorcyclists made off, but the second dropped his bike and ran away over a hedge.
The abandoned motorcycle was found to have been stolen from a property in nearby Kilnsey earlier that day.
The man, who is from Bradford, was arrested on suspicion of motor vehicle theft, failing to stop, dangerous driving and driving without a licence or insurance.
He has since been released on bailed, on the condition not to enter the Craven district while investigations are ongoing.