Not if you keep the bird caged while the cat is around. And some people even have cats and birds running/flying around together, and they remain friends, but I would never try it.
I've had parakeets for the last 10 years and cats a lot longer than that. Sometimes the cat will jump up to the chest of drawers the birds' cage is on, and he will sit there and watch the birds, and that freaks the birds out, so they start screaming at him, but he has never tried to bat at them or get into the cage etc. He just likes to watch them.

And they hate it, so the cat loses, he has to leave the room if he won't get down.
On a sad note.

When I had 4 parakeets, I used to keep their cages hanging in the living room. I guess after cleaning the cages one day I didn't put the bottom of one of the cages on tight enough or something went horribly wrong with the cage, I'll never know. While I was in the room, the bottom of the cage fell off. By the time I turned in the direction of the cage to see what made the noise (I had cleaned the cages in the morning, this was the evening) one of the parakeets flew out of the cage. Which prompted the cat to bat at the bird while it flew past him. And the parakeet did not survive. It was a horrible moment for all of us, just absolutely horrible, and it all happened within a matter seconds, maybe 3 - 5 seconds, from beginning to very tragic end.
