Not likely. You may often hear this talked about in some circles, but for most, it is just an urban legend. The practice of Karate is not illegal and promotes good citizenship.  If you commit a crime, however, you will get fingerprinted, have your picture taken and placed in the police database as someone who has broken the law. Criminals who are trained in the martial arts may experience scrutiny by the courts and be held to a higher standard due to the nature of their crime.  Breaking the law, however, has nothing to do with the practice of karate, so no, you will not have to register your hands as deadly weapons in most of the United States.
The exception to this is in the US territory of Guam.  In Title 10- Health & Safety Division 3- Public Safety, Chapter 62 in their statutes states, "Any person who is an expert in the art of karate or judo, or any similar physical are in which the hands and feet are used as deadly weapons, is required to register with the Department of Revenue and Taxation."  To register, you are required to do this in person and pay a $5 fee.  I think most of us will not have to worry about this unless we show up in Guam!