Robert De Niro -- Goodbye Mr. Jinx ... Hello Lil Bub

She can't pee in a toilet ... and you probably can't milk her nipples ... but Internet cat sensation Lil Bub is still BFFs with Robert De Niro.

"The World's Cutest Cat" and De Niro hit it off earlier today at the Tribeca Film Festival in NYC ... Mr. Jinx be damned.

De Niro's been dying to meet Bub ever since he heard she'd be featured at the festival -- telling the Hollywood Reporter, he REALLY wanted to take a picture with the deformed feline ... and De Niro always gets what he wants.

(FYI, Bub suffers from several genetic mutations including dwarfism, polydactylism, and a deformed lower jaw.)

Now, a word from Jack Byrnes on why cats are better than dogs...