Suppressors / Silencers, fall under the National Firearms Act, Special Occupation Tax. These are restricted items so be ready to wait for the ATF to process your request to purchase one. The ATF is trying to speed the process up as best they can and right now you may have to wait between 2 to 4 months after you have made your purchase. Sorry don’t shoot the messenger, if it were up to us you would have in a day.
For those of you who may still be slightly confused on the difference between a suppressor and a silencer, they are both the same. Unlike in the movies, there is no way of silencing a gun shot when the bullet travels faster then 1000 feet per second. A suppressor/Silencer will only soften the sound maybe 25db on average, this is better then nothing and on the right firearm save your hearing.