The collision happened when a white 125cc motorcycle was travelling on Lower Cherwell Street towards Upper Cherwell Street when it was in collision with a grey BMW 3 Series that was pulling out of the junction of Canal Street onto Lower Cherwell Street.
The motorcyclist, a 23-year-old man, was taken to hospital with serious injuries, including a fractured knee and fractured wrist, but he has since been discharged.
The driver of the grey BMW 3 Series stopped at the scene of the collision.
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The collision happened around 4.20pm on Sunday December 13.
Investigating officer PC Liam Calvert, of the Joint Operations Roads Policing Unit, based at Bicester, said: “This collision occurred on a stretch of road which is usually busy at that time of day, and I believe there would have been lots of vehicles on the road.
“I am appealing to anybody who was in the area and witnessed the collision, or who may have dash-cam footage, to please check this and contact police if it has captured anything that can help this investigation.
“You can make a report online or call 101, quoting reference number 43200422321.”