The animal welfare charity was alerted on July 29 when a member of the public spotted the cat with severe ailments in Woodburn Street.
The cat was taken to Graham’s Road Veterinary Clinic where it he had to be put to sleep to end his suffering.
Inspector Louise Seddon said: “The black, short haired, neutered cat was a male over eight years old.
“He was in an emaciated condition, weighing only 1.9kg when his body weight should be around 4kg.
“A post mortem examination has revealed that the cat was suffering from hyperthyroidism and a ruptured diaphragm which would have been causing him discomfort and breathing problems.
“Sadly the vet advised the best option was to put him to sleep to prevent any further suffering.
“Due to the severity of the cat’s discomfort we don’t think he would have been able to travel far and he may have been owned by someone who lives nearby to where he was found.
“We’d like to hear from anyone who may know who owned this cat to contact us as soon as possible.”
Anyone with information is being asked to contact the Scottish SPCA animal helpline on 03000 999 999.