A tabby and white cat and a lovebird and a red and orange canary were found ‘abandoned’ on Berkeley Street on the evening of January 9.
The charity said that a member of the public took the animals into their flat – but sadly, one of the birds died shortly after.
The SSPCA have said it is ‘not the correct way to give up a pet’ and are now appealing for information.
Scottish SPCA inspector, Elizabeth Lindsay, said: “Two cats, one tabby and one white, were found in a red pet carrier. A lovebird and a red and orange canary were also found alongside them in separate cages.
“The member of the public kindly took the animals inside their flat but sadly one of the birds died shortly after.
“Leaving animals outside in carriers in cold weather for a number of hours will cause them significant distress.
“We appreciate that whoever left these animals may have intended for them to be found but this is not the correct way to give up a pet if you can no longer care for them.
“The cats and bird are now in the care of one of our animal rescue and rehoming centres and receiving the appropriate treatment.
“If anyone recognises these animals or has any information surrounding their circumstances, they should call the Scottish SPCA confidential animal helpline on 03000 999 999.”