No, rimfire guns are not required to be registered with a suppressor. However, if you wish to add a suppressor to your rimfire gun, you must first register the gun with the National Firearms Registration and Transfer Record. You can do this by sending a completed Form 4 application to the Alcohol, Tobacco, and Firearms Division of the U.S. Department of Justice. There is no fee for registering your gun.
When you have registered your gun, you may then purchase a suppressor from any licensed firearms dealer. The process for purchasing a suppressor is the same as purchasing any other firearm: you must complete a background check and submit fingerprints and photographs to the ATF. You will also need to pay for a $200 tax stamp.
If you already have a gun that is registered with a suppressor, you may transfer the suppressor to another gun by completing a Form 4 and sending it to the ATF. There is no fee for this transfer.
You may not possess a suppressor if you are under the age of 21, if you have been convicted of a felony, or if you are a fugitive from justice. Additionally, some states have laws regarding the possession of suppressors. Be sure to check the laws in your state before purchasing or possessing a suppressor.