The road was closed for most of the day while emergency services rushed to the scene. It later reopened at 8.20pm.
The male rider, who is in his sixties and from Bristol, was taken by air ambulance to Southmead Hospital with life changing injuries.
The rider is currently in a critical but stable condition. The male driver and passengers of the Audi, who were also from the Bristol area, were shaken but uninjured.
Wiltshire Police are appealing for anyone who may have witnessed the collision or saw the car or bike beforehand to contact 101, quoting reference number 54210031542.
If you have a dash cam and were in the area at the time, they would ask you to check the footage in case you have collected evidence which could be useful to their investigation.