Yes, air gun suppressors are legal in the United States. There are a few steps you need to take to purchase and use one though.
First, you need to find a licensed dealer who sells them. There are only a handful of these dealers in the country, so you may have to do some research to find one near you.
Then, you need to apply to the ATF (Alcohol, Tobacco, Firearms, and Explosives) along with a $200 tax stamp. This is called a Form 1 application. The process can take several months for the application to be approved.
Once you have received your approval from the ATF, you can then purchase your air gun suppressor and use it by all state and federal laws.
There are a few states that have additional restrictions on air gun suppressors, so be sure to check the laws in your state before purchasing one.