The animal was found in the Priory Close and Hills Close area of the village on Saturday, February 19.
The cat’s leg had been snared in a gin trap, causing tissue damage.
The traps have been illegal in the UK since 1958. They are designed to catch animals by their legs, using spring-operated jaws with teeth or a serrated edge.
Police are appealing for information. Contact PCSO Paul Bailey, from Swaffham safer neighbourhood team, on 0845 456 4567.
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