Answer:
If you mean a silencer for a handgun, it depends. Silencers are legal in most U.S. states, but must be purchased from/through a licensed class III dealer. If you have done this, you will have paperwork proving you can legally own the silencer. If you don't have that, or if you are in a state where silencers/supressors are illegal, yes, you can be arrested.
Another View: Use the above information with caution. Possession of a silencer falls under the same federal statutes as possession of an automatic weapon or sawed off shotgun. YOU must have a federal permit to possess one . . . for pretty OBVIOUS reasons.
It isn't a permit, it's a tax stamp. You must apply and receive a separate tax stamp for each item you own and must keep the stamp or a copy of it with the item at all times. For instance, if you have a short barrelled rifle with a supressor, then you must have two tax stamps, one for the rifle and one for the supressor, each costing $200. If you have three short barrelled rifles and three supressors, you must have six tax stamps, one for each, still at a cost of $200 each. If you sell the items, then the buyer must apply for his or her own stamp for each item. The stamps are not transferable.