Why the heck do out-of-state lawyers answer questions with "I don't know about California, but in my state..." when they could just Google the answer?
The answer to your question is in California Business and Professions Code 6067:
"Every person on his admission [to the State Bar] shall take an oath to support the Constitution of the United States and the Constitution of the State of California, and faithfully to discharge the duties of any attorney at law to the best of his knowledge and ability. A certificate of the oath shall be indorsed upon his license."
Strangely, the oath does not appear on the certificate from the California Supreme Court that says I was admitted or on my bar card.
The answer in my jurisdictions is yes.
This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Laws vary widely from state to state. You should rely only on the advice given to you during a personal consultation by a local attorney who is thoroughly familiar with state laws and the area of practice in which your concern lies.