There is. If you want a non stop train, Trenitalia will sell you a Leonardo Express ticket for 14 euro each way. Double that for 2 pax and personally I'd rather pay the premium to have a car pick me up and drop me off, especially with luggage.

If you google train rome to fco you'll get all the detail you're looking for.

http://www.trenitalia.com/tcom-en/Se...micino-Airport

If you're looking for something as inexpensive as possible, google for bus service from rome to fco. There are a number of them, mostly going direct from one of the main train stations to the airport.