John Fairley, 21, made the discovery near a bridge over the canal, close to the Asda Chesser supermarket, at around 7pm on Thursday evening.
He told the Edinburgh Evening News: “I was in shock when I found it. I’m really chuffed with the find.”
Firearms expert Mark Mastaglio, director of London-based Forensics Firearms Consultancy, said: “The intrepid angler has caught a Second World War, American 0.50 Inch (.50 Cal) machine gun round of the type that was used on numerous US aircraft both fighters and bombers.
“It was made by Twin Cities Ordnance plant in Minnesota in 1943 and could well have fallen from the sky. However if live, and a sealed round of ammunition could still be live even if it has been submerged in water all these years, it will be subject to Firearms Certificate control.”
Mr Fairley, who lives in Parkhead, said he had been contacted by a magnet fishing community in the US who were interested in seeing the photographs of his find.
It comes two weeks after part of a shotgun and two cartridges were pulled out of the canal under the Viewforth Bridge.
Police recovered the weapon which is thought to be the remains of a pump action shotgun and is incapable of firing.
Magnet fishing is similar to metal detecting and involves using magnets attached to the ends of ropes to recover metal objects dumped in canals and rivers.