The call comes after a man was convicted in an Adelaide court for using the trap in his backyard to catch his neighbour's four-year-old cat, Lunar.
The 71-year-old admitted to police he was aware she was in the trap for about two hours "but left her meowing in pain", RSPCA South Australia said in a statement on Sunday.
After the injured cat was freed, an RSPCA inspector and police attended the man's property to find the steel-jaw trap had been reset.
It had been set next to a hole in a fence and surrounded by brickwork, funnelling cats entering through the hole to walk directly into the trap.
"These are barbaric devices that inflict terrible injuries and cause enormous suffering," RSPCA SA Chief Inspector Andrew Baker said.
"It's tragic to think that some animals could become trapped and never found, leaving them to die in agony."
Mr Baker hoped the prosecution of the man, convicted of animal cruelty and setting a steel-jaw trap, would deter others from using them.
"From RSPCA's perspective, there's no good reason to own a steel-jaw trap," he said.
"We encourage anyone who has one to turn it into scrap metal so that there is no possibility of it ever falling into the hands of a person who wants to harm animals."
According to the RSPCA, the man was placed on a six-month good behaviour bond on Friday and ordered to pay Lunar's vet costs, exceeding $4000.
One of Lunar's toes was crushed by the trap and required amputation.
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