Of course you can have a cat and a bird - lots of people do.
First of all, if you are getting a handfed bird that is already tame and not afraid of people, then it will probably be unafraid of the cat as well (unless it has a prior bad experience with a cat, of course). Seeing the cat will not cause it stress, but it does mean that it's especially important that you keep it safe from the cat.
How you keep them together depends on your cat's personality... basically, is your cat a hunter? If you have a determined hunter, then it's a little harder to keep a bird safe. You will almost definitely need to keep them separate rooms. The bird might be able to be in a secure cage while the cat's in the room if you can keep an eye on them.
If you have an easy going cat that is uninterested in birds, then you can probably have the cage in a room that the cat has access to. You might even be able to have the bird out at the same time as the cat, but this does require close supervision. A bird that is startled into flight or fluttering can awaken a hunting instinct in an otherwise lazy cat.
Also, you'll want to get a large, sturdy cage with smaller bar spacing (to keep paws out, just in case) - basically something like a flight cage or larger, no wire cages with doors that a cat or bird could slide up. And I would recommend also getting one of those treat dispensers that cats roll around, so that if the kitty needs to spend time locked up in another room, at least he can be entertained and happy.
My own experiences with cats and birds were with a pretty lazy cat who was already about 7 years old when I got my first bird, my GCC. He showed a little interest in her, but since she wasn't scared of him and didn't act like 'prey', he quickly lost interest in her. I have to admit, I got pretty casual with them over the years. They were nearly always loose in the house together when someone was home; I would usually shut the birds in the bird room when no one was around, but sometimes the cat would be asleep in the bird room in the closet or some other hiding place, and I'd miss him and accidentally lock him in there with the birds. And then, there was one time I went away for the weekend and had a pet sitter. The birds were supposed to stay locked in their room and the cat in the rest of the house; well my GCC must've flown out and the bird sitter missed it, so I came back with my GCC locked out of her bird room with the cat. Not only that, but she'd apparently tried to fly back to the bird room when the rest of the house got dark, and I found her on the floor in the hallway outside her room - very hungry and very happy to be picked up off the floor, but otherwise just fine. The cat finally passed away at age 19, and he never harmed or tried to harm a bird.
I wouldn't recommend this; I had an especially easy-going cat, and even so, I lucked out. But cats are not always quite the danger people make them out to be. Some older parrot books even recommend getting a cat to help keep a parrot company during the day! On the other hand, though, if you have a cat who's a hunter, it's virtually impossible to train that tendency out of them and they can never really be trusted.
