Rayhan Qadar, 21, from Eastville, or Ray Pew as he is known on Twitter, issued an apology four hours after his initial tweet sparked outrage.
He said: "My previous tweet about the cyclist was obviously not true. I did not hit cyclist. Not today. Not ever. A bad joke on my part it seems."
Earlier in the morning, Mr Qada, whose Facebook and Twitter profiles say he is from Bristol, caused a furious backlash after tweeting: "Think I just hit a cyclist. But Im (sic) late for work so had to drive off lol."
Police said they were investigating the matter. Mr Qada added: "Sorry if anyone thought i actually hit a cyclist. Anyone who follows me on Twitter know 99% of the things I tweet is nonsense."