Cats need to have a health certificate from a veteranarian no more than 10 days prior to the flight, and a documented rabies shot within the last one (or maybe it's two) years. This is actually for the airline. The US government doesn't really care.
You also need to make a reservation with the airline for your cat, as most airlines only allow a few cats to ride in the cabin per flight. And expect to pay about US$90-150 for the cat's "ticket", depending on the airline. They count as excess baggage, and are your carry-on, so don't plan on bringing another backpack on with you.
Also, be prepared to take the cat out of the bag (hehe) for security checks, which is a royal pain (literally) if your cat is like mine, and claws when scared.
I would also recommend bringing a change of clothes for yourself. My cat pissed in her bag in Japan, and I had to take her out and clean the bag and cat, which left me a little pissed on. But I was prepared, so the people sitting near me on the plane didn't notice.