Jonathon Leslie, 23, a St Andrews University student, was found with the decapitated bird in his car after being caught drink driving.
Leslie, from Aberdeen, was fined a total of Â£750 and banned from driving for a year.
He killed the bird on 10 September at Abbey Park in St Andrews.
The court heard geoscience and French student Leslie had been watching the Last Night of the Proms on TV with friends after drinking wine with his dinner.
The group, all students at St Andrews University, then decided to take candles and explore the derelict Abbey Park House mansion in the centre of the Fife town, claiming to be "interested in the architecture".
Fiscal depute Brian Robertson told Cupar Sheriff Court: "Without warning the accused was seen to seize hold of a pigeon that had taken flight as a result of being disturbed.
"He then pulled the head from the bird, causing its instant death. Police were contacted after security staff noticed the accused and others on CCTV.
"The accused admitted responsibility for it and appeared to believe he had done nothing wrong. He smelled strongly of alcohol and had been driving."
Defence lawyer Gregor Kelly said Leslie's father had flown in from Azerbaijan - where he works as an oil industry executive - to support his son at the hearing.
Mr Kelly added: "It was an impulsive act. It was a moment of bravado and nothing more that he said he would eat it as it would have been a waste otherwise.
"He deeply regrets the suffering he caused to the bird and hopes the events of this sorry evening don't impinge on his future career."
A Fife student has admitted catching a wild pigeon with his bare hands and ripping its head off during a night out.