Firearms sold through California Federal Firearms Licensees (FFLs) generally are recorded with the state through the Dealer's Record of Sale process. (Penal Code 12070 and following)
However, sales using an FFL were not required until January 1, 1991. Prior to that date an individual could sell to another individual without using a dealer, and there are probably several million firearms in California which have not changed hands since 1990.
Beginning January 1, 1998, individuals moving to California with handguns are required to register their handguns as "personal handgun importers" (Penal Code 12072(f)(2)). The person must file the "New Resident Handgun Ownership Report".
Prior to 1998, guns moved here were not registered, even by mail. Note that this registration requirement does not apply to "long guns", typically shotguns and rifles. The number of firearms moved here is unknown.
Infrequent sales of long guns over fifty years old are exempt from using an FFL (Penal Code 12078 (t)(2)). (Infrequent means "occasional and without regularity.", Penal Code 12070 (c)(1))
The net effect of these older guns is not all guns in California are registered with the state, and it is not required that they be registered.
An individual may ask the California Department of Justice, Bureau of Firearms, for a report of all firearms registered to him or her by filing a "Automated Firearms System (AFS) Records Request Form".
An individual may voluntarily register a firearm with the state by filing a "Firearm Ownership Record".