Cal. Rev. & Tax. Code § 7232
(g)
(1) Fees contained in this chapter shall not apply to a motor carrier of property while engaged solely in interstate or foreign transportation of property by motor vehicle. A motor carrier of property shall not engage in any interstate or foreign transportation of property for compensation by motor vehicle on any public highway in this state without first having registered the operation with the Department of Motor Vehicles or with the carrier’s base registration state, if other than California, as determined in accordance with final regulations issued pursuant to the Federal Unified Carrier Registration Act of 2005 (P.L.109-59). To register with the Department of Motor Vehicles, carriers specified in this subdivision shall comply with the following: