One-year-old Teenie was found injured by her owner Sarah Nisbett in Niddry View, Winchburgh, West Lothian, at around 4.30pm on Friday and taken to the SSPCA.
She had been shot twice in the shoulder and once in her left rear leg, which was so badly damaged that vets had "no option" but to amputate it.
Mrs Nisbett said the cat is now having to learn how to walk again.
She said: "The gun that was used must have some power because the pellet actually went through her back leg, that's why it was so badly damaged.
"She's now learning how to hop around the house, it's terrible.
"The fact that it was three shots is crazy, we live in a housing estate and there are lots of kids. That just makes it worse because any of them could have been hit in the crossfire.
"There's some sick people out there, hopefully somebody will know who's done this and let the police or SSPCA know."
The SSPCA said Teenie is "incredibly lucky" to have survived the attack.
Chief Superintendent Mike Flynn said: "Teenie's owners are understandably very upset and keen for us to find the callous person responsible to ensure no more cats come to harm.
"This is an alarming incident which only highlights why the Scottish Government should implement the licensing of airguns as a matter of urgency.
"The new licensing regime should ensure that only those with a lawful reason are allowed to possess such a dangerous weapon. It will also help the police trace anyone using an air gun irresponsibly.
"We are urging local pet owners to be vigilant and appealing to anyone with information to search their conscience and contact our animal helpline."
Last year the Scottish Government launched a consultation on licensing air weapons, with a large majority of those who responded opposing the plan.
Under the proposed scheme, anyone wanting to own an air gun would need to demonstrate they had a legitimate reason for doing so.
A total of 87% of respondents rejected the idea - with some describing it as "draconian" and "heavy-handed". A small number of people felt ministers were not going far enough.
The SSPCA is appealing for anyone with information on the shooting incident to contact it on 03000 999 999.