Yes, a DUI conviction out of state will affect your California license. Ohio and California are both members of the Drivers License Compact (DLC) which requires member states to report to other member states traffic violations their licensed motorists received out of state. This is the same agreement that Florida is also a part of.

According to the CA Vehicle Code, section 13363, the California Department of Motor Vehicles may suspend or revoke the privilege of any resident or nonresident to drive a motor vehicle in this State upon receiving notice of the conviction of the person in a state, territory, or possession of the United States, the District of Columbia, the Commonwealth of Puerto Rico, or the Dominion of Canada of an offense therein which, if committed in this State, would be grounds for the suspension or revocation of the privilege to operate a motor vehicle.

As part of VC that mentions the DLC section 15023 states that the licensing authority in the home state, for the purposes of suspending, revoking, or limiting the license to operate a motor vehicle, shall give the same effect to the conduct reported, it would if such conduct had occurred in the home state, in the case of a conviction for certain offenses.

Listed here specifically is driving a motor vehicle while under the influence of intoxicating liquor or a narcotic drug, or under the influence of any other drug to a degree which renders the driver incapable of safely driving a motor vehicle.

In CA a DUI first time conviction of a DUI typically results in penalties such as jail time, fines, vehicle impoundment, license suspension for 6 months or more, and a completion of a DUI program. So it appears you may receive these penalties as well as the penalties handed down from Ohio.