From website cited:

Game and Hunting Trophies
If you plan to import game or a hunting trophy, please contact the Fish and Wildlife Service before you leave at (800) 358-2104 . Currently, 14 Customs ports of entry are designated to handle game and trophies; other Customs ports must get approval from the Fish and Wildlife Service to clear your entry.

Depending on the species you bring back, you might need a permit from the country where the animal was harvested. Regardless of the species, you’ll have to fill out a Fish and Wildlife form 3-177, Declaration for Importation or Exportation.

Trophies may also be subject to inspection by the U.S. Department of Agriculture’s Animal and Plant Health Inspection Service (APHIS) for sanitary purposes. General guidelines for importing trophies can be found in APHIS’s publication Traveler’s Tips. Contact USDA-APHIS-PPQ, Permit Unit, 4700 River Road, Unit 133, Riverdale, MD 20737, or call (301) 734-8645 .

Also, federal regulations do not allow the importation of any species into a state with fish or wildlife laws that are more restrictive than federal laws. And if foreign laws were violated in the taking, sale, possession, or export to the United States of wild animals, those animals will not be allowed entry into the United States.

Warning: There are many regulations, enforced by various agencies, governing the importation of animals and animal parts. Failure to comply with them could result in time-consuming delays in clearing your trophy through Customs. You should always call for guidance before you depart
References :
http://www.internationalbenefits.com/customs-prohibited-items.htm

you would probably have to take it to a taxidermist their in that country and then ship it in to the U.S.
References :

I would strongly recommend not to bring them. It’s probably legal, but it’s a huuge inconvenience and time-waster to have to declare ANYTHING in customs, especially anything that needs to be closely inspected. There’s a good chance it would just get confiscated if the customs people on duty didn’t know what to do with it.
References :
too many flights to/from the US and too many hours of waiting in customs lines reading immigration & customs posters behind people bringing the most random stuff EVER that needs to be inspected into the US.