The animal, nicknamed Curiosity, had to be put down by vets due to the severity of the injuries caused by the device.
It was found off Wood Lane in Burgh, near Aylsham, on Saturday by RSPCA officers who said the animal was in a distressed state.
The male tabby was feared to have suffered brain damage and its claws had worn away from attempts to escape from the trap.
A spokesman for RSPCA today confirmed that Curiosity had been put to sleep by vets at Companion Care, in Longwater.
“Very sadly, they could do nothing to save her as the damage was to severe, “ the spokesman said.
“The vets said for welfare reasons they could not do anything to save her, and so she had to be put to sleep to prevent further suffering.
It had been hoped that the animal would recover as a potential new home had already been found.
The RSPCA said Curiosity did not have a microchip and its owners were unknown.
Information is still being sought as to where the Fenn Trap came from and who set it.
Llewelyn Lowen, scientific officer for the RSPCA, said: “There are strict legal conditions on setting these types of traps and not setting them in the right way can mean that you are committing an offence.
“These traps should be set in such a way to prevent them killing or injuring a domestic animal and so we urge people to think carefully before using them.”
A Fenn trap is a spring trap commonly used for catching wildlife including grey squirrels, stoats, rats and mice.
RSPCA inspector Dean Astillberry said: “This poor cat had somehow got his head completely stuck, face-down, in this lethal trap. We don’t know how long he would have been wandering about like that.
“His face was swollen out of all proportion. He could not open his eyes at all, and his mouth just a small distance.
Anyone with information about the owner of the trap should contact the RSPCA on 0300 123 8018.