The accident took place in Winchburgh, West Lothian on Thursday 24 March.
The blue hatchback with roof rails turned into Niddry Road at around 2pm and knocked down the 42-year-old cyclist.
The driver then took off without checking that he was okay.
A police spokesperson said: “We are appealing for anyone who may have been in the area about 2pm on Thursday afternoon.
“It may well be that the driver of the vehicle was unaware that they had collided with the cyclist, and so we would urge them to come forward themselves.”
Anyone with information is asked to contact Lothian and Borders Police on 0131 311 3131, or the charity Crimestoppers in confidence and complete anonymity on 0800 555 111.