Jasper, a five-year-old ginger tom, belongs to the deputy librarian at the Marshall Library of Economics.
He became a hit with students after his owner took him to work, and a recent "tea with Jasper" event attracted 140 moggy-lovers.
Similar events are planned as Jasper is now the library's "official mascot".
Jasper lost his left hind leg in a car accident and was abandoned by his owners. He was adopted by deputy librarian Simon Frost from a rescue centre.
While the cat is well-behaved on university premises, spending his time browsing the shelves and sleeping on copies of the Financial Times, Jasper is more adventurous on his home turf.
"He's bouncy like Tigger, because he has three legs, and he's a bit unstable when he moves slowly - so he goes everywhere at speed," Mr Frost said.
Jasper also likes to climb trees, "but he can't get down", he added.
Librarian Clare Trowell said: "Students coming to visit and pet Jasper told us just how much he'd calmed them down, and helped relieve any stress.
"Many of them were missing their own cats or other pets."
Jasper now has his own hashtag - #economicscat - and frequently makes announcements about the library on social media.
There is also a university "cat club" on Facebook, where students who are missing their pets can share photos of them with other cat lovers.
A three-legged cat adopted by a Cambridge University library is being used to help relieve students' stress during the exam season.