The incident happened last week.
The Scottish SPCA said the black and white kitten, called Pixie, was left on a wall on in Grahams Road, around 9:30pm on Tuesday, March 30.
A member of the public saw a man put it there and then run off.
Now the animal welfare charity has appealed for people to come forward with information.
The pet was just a few months old and not micro-chipped
Robyn Myszor, Scottish SPCA inspector, said, “A member of the public witnessed a man walking along the street with the cat on his shoulder.
“He then put the cat down on the wall outside a block of flats and ran away down an alley next to the nearby Mario’s takeaway.”
The inspector said the man was around 5”8 with short hair, and appeared to have been drinking. “He was holding a can of something at the time of the incident. He stated to some bystanders that the kitten’s name was Pixie.
“We appreciate that the man who left the kitten may have intended for the animal to be found but this is not the right way to give up an animal if you can no longer care for them.”The Scottish SPCA said the kitten was unharmed and is now in the care of one of its animal rescue and rehoming centres.
Contact its confidential animal helpline on 03000 999 999.