Yes. California requires you to be fingerprinted and a background check. This is done through the company that California has authorized. You may obtain your fingerprints throughout California at Accurate Biometrics locations. Preregistration is required. The fee to be finger printed is $68.95 (subject to change). Also, fingerprinting can be done at Live Scan Fingerprinting Vendors and at PSI locations (Prices varies depending on location).
Registration Website (Preregistration required)
Tip: Try to plan your fingerprinting after you pass your exam and immediately before you apply for your license because the Fingerprint data is valid for 1 year. See here.