Cottle, 22, of East Sussex, who was driving his girlfriend’s car when the incident occurred, had admitted a public nuisance charge at Maidstone Crown Court.
The BBC reported that Judge Martin Joy told the defendant, of Durgates, Wadhurst, he had “endangered many lives”.
He said Cottle’s actions were “premeditated” and inexcusable”.
Jonathan Palmer, chief executive of MSV – the firm that owns Brands Hatch – said Cottle’s “reckless act” endangered the lives of the racing car drivers, the track marshals and everyone in the vehicle he was driving.
“His idiotic and selfish behaviour – aggravated by his unrepentant attitude in subsequent media coverage – received much immediate condemnation,” he added.
“His conviction and prison sentence will serve to reinforce the message that this kind of antisocial behaviour is not only stupid, but will lead to prosecution.”