The young adult female cat was found on Saturday 2 February near a park and some woods off Atterby Drive.
The finder kindly took her home and called the RSPCA for help.
RSPCA inspector Ben Cottle-Shaw said: “I picked up this lovely cat from the person who found her.
“She was underweight and had severe fur loss.
“She has been seen by a vet who has confirmed that she is suffering from a flea allergy and worms.
“I suspect she has been dumped and we want to hear from anyone who knows who she belongs to.
“She wasn’t microchipped and was not wearing a collar so at the moment there is no way of tracing her owner.”
Anyone who recognises her, or has any specific information that might help our investigation, should call the RSPCA inspector appeal line on 0300 123 8018 and ask to leave a message for Inspector Cottle-Shaw.
He added: “She has already improved in the care of the wonderful staff at RSPCA Doncaster & Rotherham branch - where she has been named Sophie. She’s really friendly and affectionate and if no one comes forward she will be rehomed when she’s better.”