Tahir Chaudhry, 34, swerved his van at the bike after clashing with the cycle courier at traffic lights. The father-of-two then drove off after the collision leaving the concussed victim behind.
Passers-by went to the aid of courier Greig Walker, 34, and also noted the registration number of Chaudhry's vehicle.
Mr Walker had five stitches put in wounds and suffered multiple cuts and bruises in the incident.
The High Court in Edinburgh heard yesterday that it was fortunate he was wearing a helmet when he was knocked to the ground.
Lord McEwan told Chaudhry that he took into account his good background and references provided on his behalf.
But the judge said: "Nonetheless, I think in the public interest to suppress road rage I have to pronounce a custodial sentence."
"I have to take a very serious view of this matter which is a very bad example of road rage."
Lord McEwan also banned Chaudhry, of Colinton Road, Edinburgh, from driving for five years and ordered him to resit a driving test.
Chaudhry, the manager of a family-run store business, was originally charged with attempting to murder Mr Walker.
But the Crown accepted his guilty plea to an alternative charge of driving dangerously and causing a collision which left the victim unconscious and severely injured. The offence carries a maximum penalty of two years imprisonment.
The court heard that cycle delivery courier Mr Walker received a job on November 3 last year which took him from the West End of the Capital to the Wester Hailes area. Chaudhry's van undertook him at a junction and went across his path. Mr Walker shouted at the driver as he felt that he had been cut up.
The van was ahead of him on Wester Hailes Road but did an emergency stop and reversed towards him. As the van picked up speed the cyclist decided to take evasive action and mounted a verge. He continued on his way and came back onto the road ahead of the van. But as he cycled on he could hear the van picking up speed. The court heard witnesses saw the van swerve deliberately towards the bike, clipping it and throwing the victim to the ground.
Defence counsel Sarah Livingstone urged the judge not to jail Chaudhry who was assessed as being a very low risk of re-offending.