The dramatic video shows Deliveroo cyclist Daniel Smith hurtling over the roof of the Nissan Note at the junction of Grange Road and Causewayside.
Police have confirmed that they are investigating the incident.
He broke his coccyx and suffered minor head injuries after slamming into the road on Saturday night.
“A reminder for me how vulnerable cyclists are cycling in a city. And if there is anything anyone can take from this is, just please look for cyclists when you are driving,” Mr Smith later posted on Facebook.
Footage caught on the dashcam of a car stopped at lights shows the Nissan turning right in the rain apparently without spotting Mr Smith.
The physics student was wearing a white and teal coloured florescent jacket, yellow trainers, and black shorts, as well as a green Deliveroo takeaway bag.
The video shows him crashing into the front of the car at speed and onto the roof, ending up on his back.
He then slides, legs in the air, to the road. The clearly shaken up driver and her passenger then get out of the car to check if Mr Smith is ok.
Mr Smith is then seen bending over in pain as the driver speaks to him.
He later told how he suffered a few close calls while cycling but this incident had “shocked” him.
“I was actually on my way to pick up another delivery after just finishing my last delivery down the road,” said Mr Smith.
“Sitting down hurts a lot and there is nothing they can do about it when I’m doing my resit exams, so I’m in the process of looking at special circumstances for my exams as I’m so shaken by the accident and my head is everywhere.
“Luckily I’m ok and heading to hospital now, but it could have been much worse for me!
“Obviously I’m not going to be able to work for a while now so for me the impact is much greater than just a bump and a scare.”