Inspectors were called to a property in the outer rural suburb of Henley Brook on Sunday after a woman reported the injured animal was in her garden.
The RSPCA said it appeared the cat was set on fire and also had a broken tail and other injuries.
The cat is on pain relief medication and is being treated for its injuries.
It follows other recent acts of animal cruelty including a horse that was shot with a shotgun, and a kangaroo and dog that were shot in separate incidents with an arrow.
“It is appalling that the RSPCA has investigated four deliberate acts of animal cruelty inside of three weeks,” RSPCA chief executive David van Ooran said.
Anyone with information about any of the incidents is asked to call the RSPCA’s cruelty hotline on 1300 278 3589.