How many registered guns are in the US?

Unless stolen before making it to a retailer, they all are when bought.

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Firearms are not registered when sold by retailers (FFL dealers) unless they are required to be registered in a particular state. And the registration is usually done by the local police department in those states.

FFL dealers record the buyer's information from form 4473 in their "bound book" and then they are obligated to keep these records for as long as they remain in business and keep their federal firearms license renewed.

Gues it all depends on what the OP meant by "registered"