They already do...
The voter registration rolls (lists of registered voters) are not available to the general public. However, California law allows certain voter information to be released to a member of the California Legislature or U.S. Congress, or to any candidate, any committee for or against a proposed ballot measure, any person for election, scholarly, journalistic, or political purpose, or for governmental purposes. Even in these cases, your social security number, driver license number, and signature will remain confidential.
http://www.sos.ca.gov/administration/privacy-policy/