Yes, silencers in the US are a federally registered item, require an approved ATF Form 1 to make or an ATF Form 4 to transfer registration to a new owner. Silencers are "firearms" under the 1934 Nation Firearms Act (now called Title II of the federal gun control act, conventional firearms falling under Title I formerly known as the 1968 Gun Control Act). Registration tax is $200.
In other countries usually thought to be more restrictive than the US, silencers (mufflers, sound suppressors, noise moderators) are treated as firearms accessories with little or no restriction, even in jurisdictions like the UK where guns are strictly controlled.
People keeping shotguns in England for pest control have actully been advised by the local constabulary to use silencers to avoid unneccessary "shot fired" police calls.
Finland advises use of silencers to avoid hearing loss. France has reasonable regulations on silencers also. Hiram Maxim's first silencer was advertised and sold for sporting use in the early 1900s.