The charity was called to investigate after the cat returned home to Drum Brae Crescent on 11 May.
An undercover officer said: “The cat lost three claws and suffered abrasions to his face, tongue and paws.
“We are urging other pet owners in the local area to be on their guard.
“Snares are generally designed for rabbits, foxes and hares. However, in this environment it is likely this snare was set intentionally for cats.
“This homemade snare was untagged and non-locking, both of which constitute offences under the Snares (Scotland) Order 2010.
“Our enquiries so far have not resulted in any leads and we are now urging anyone with information about this incident or other cases of illegal snaring to contact our Animal Helpline on 03000 999 999.”