A section from the book "Hypnotism: How It Is Done; Its Uses And Dangers" (by James R. Cocke) called Hypnotism In The Lower Animals details about an experiment done which concludes how a bird can be fascinated by looking at a cat's eyes.
While it may somewhat suggest that cats could possibly have that ability, felines have no power to hypnotize its prey.
The ability that a cat can hold the attention of a bird is familiar to all, but what often happens is that the prey instinctively "freezes" when a predator is nearby in the hope it won't be noticed.
Cats have a number of unusual abilities, but hypnosis is not one of them.
Check out Cats Superhuman Abilities That Appears Like Magic featured on Mercola.com.