For domestic flights, there is no such requirement. Pilots may still file the type aircraft designator they are accustomed to when remaining inside the United States.
For an unspecified amount of time the Automated Flight Service Stations (AFSS) will translate aircraft designators to the ICAO format for pilots. Pilots are encouraged to learn their designator immediately so as not to rely on the Flight Service for the translation.
The following file is an FAA publication that displays the ICAO designator for aircraft types. There is a listing of both Rotorcraft and Fixed-Wing. ICAO recently updated their Designator list and the FAA publication shows the old ICAO as well as the new.
Remember, if you fly inside the United States, you can still file the aircraft designator you have been filing. This only applies to flight plans files to international destinations.