Stewart Murray, 48, followed and filmed Constable Jennifer Sneddon until she fled in tears into a police station and collapsed in front of colleagues.
The former paramedic and army officer targeted the officer after her patrol van struck a young rugby player, leaving him disabled. Sheriff Brian Murphy fined Murray £400 and told him: "Your vendetta against against PC Sneddon must stop now or you will be in serious trouble."
PC Sneddon, 34, said she was "terrified" of Murray, who videoed her in the street while she was on trial for careless driving following the accident on the Isle of Arran.
"I was frightened by his actions and his abusive language and terminology," she told Kilmarnock Sheriff Court.
"He continued with a tirade of abuse and derogatory remarks. He raised his voice and became aggressive and his tone changed dramatically."
The officer - who was found not guilty - said Murray told her: "I'm in a public place and I can do what I like."