Snoop was rescued by the charity earlier this month when his owners were unable to afford his ongoing veterinary costs.
The 10-week-old pup has been at the RSPCA's Doncaster & Rotherham branch for two weeks.
Natalie Flanagan, from the branch, said: 'Snoop is an adventurous little puppy who has melted the hearts of everyone who meets him!
'He's such a lovely, friendly and happy little dog and he really deserves to have a chance in life.
'Unfortunately, he has a rare condition and needs life-saving surgery so he can see his first Christmas.'
Terrier Snoop has a medical condition called megaesophagus, meaning his oesophagus does not function properly, so he cannot get food into his stomach easily.
'This is a congenital abnormality of the heart's blood vessels resulting in the oesophagus being compressed. This prevents Snoop from being able to eat solid food. Because the food is not moved properly through the oesophagus it can cause him to be sick or potentially choke,' Natalie added.
'Snoop requires surgery as soon as possible to repair this condition. This is a tricky and costly procedure so we're asking for support from you. Getting Snoop the help he needs will be the best Christmas present he - and everyone here at the RSPCA - could ask for!'
In the meantime, staff have to ensure Snoop eats slowly and from a raised platform. They feed him by mashing up his food with warm water - to create a soup-like consistency - and pour it into an elevated slow feeder to help him digest.
Once the branch has raised enough funds for Snoop's surgery he will be able to have his operation and, once recovered, can begin his search for a loving new home*.
To donate to Snoop's appeal please visit: www.rspcadoncasterrotherham.org.uk/appeal/snoop.
Snoop is just one of the animals being looked after by staff at RSPCA Doncaster and Rotherham and an example of why the branch needs funds for vet fees. Any excess funds generated from this appeal will go towards veterinary treatment for other animals at the branch.