It happened on the southbound carriageway between Stow and Galashiels close to the B710 junction for Clovenfords at about 18:00 on Thursday.
The 66-year-old man was signalled to pull over by a van driver and the two became involved in a dispute.
The suspect then punched the man and smashed his pick-up's wing mirror.
The victim sustained minor facial injuries but did not require medical attention, police said.
He was driving a silver Hyundai iload pick-up vehicle and the van involved was white and green.
PC Sarah Younger from Galashiels Police Station said: "This dispute and subsequent assault seems to have been over a relatively minor issue, but resulted in the victim being assaulted and his vehicle being damaged.
"I would ask that anyone who was on the A7 on Wednesday evening and witnessed this exchange, or who has information that can help us identify the suspect, contacts police immediately."
Police have appealed for witnesses after a man was punched in the face in a road rage incident on the A7 in the Scottish Borders.