The incident happened when the 73-year-old victim, who is from Birstall, was approached by two men while waiting for a bus at the junction of Pearl Street and Bradford Road in Batley on Tuesday March 22 at around 1.30pm.
One of the men asked if the victim could change some coins and produced change from his pocket before they exchanged money.
It was only when the elderly victim returned home that he realised the man had pulled his wedding ring from his finger.
PC Darren Hill, of West Yorkshire Police, has launched an appeal for witnesses in a bid to track the thieves.
He said: “Clearly this would have been an extremely upsetting offence for the victim at any time of year but for it to happen on his 50th wedding anniversary has only made the circumstances even more upsetting.
“I would ask anyone who saw this offence or may be able to help us identify these two men to come forward.
“We would also advise residents in the Batley area to be wary of this kind of scam.”
The first suspect was described as 6ft tall, fat and balding with a lump under his right eye. He also had an eastern European accent.
The second man was white, 5ft 6ins tall, slim, and had an olive complexion. Both the suspects were white.
Anyone with information that may help police track the suspects is urged to call Batley Neighbourhood Policing Team on 101, quoting crime reference number 1316026319, or Crimestoppers anonymously on 0800 555111.