The incident, which took place in Ferry Road at about 1.30am yesterday (Sunday, June 19), involved a blue Nissan Note vehicle, police said.
Police added that a 55-year-old man was arrested on suspicion of attempting to cause grievous bodily harm and has been bailed, pending further enquiries.
Officers are now appealing for witnesses and anyone with information or footage, including CCTV or dashcam footage, to contact them as part of their investigation.
Investigator Bernadette Peters, from Sussex Police, said: “We know that there were a number of people in the area at the time near the Crown Inn pub, and want to encourage them to come forward with information about what they saw or what happened.”
Police said information about yesterday’s incident in Rye can be reported to Sussex Police online or by calling 101 and quoting serial 96 of 19/06.