Has Stanford ever been given the option to join the University of California system?

I don’t know, but I’m sure if they were made such an offer they would refuse it (if they haven’t done so already).

I doubt it, why would they? Their funding and administration are completely independent of the State of California.
The U.C. system is state-funded and answerable to the Regents of the U. of C.
Stanford has its independent endowments and can make different kinds of decisions than they could if they were in the U.C. system.

I can’t think of a reason why Stanford would want to fold themselves into the U.C. system, and not that the U.C. has much against Stanford besides some healthy sports rivalries there isn’t much reason to think pulling Stanford into the U.C. system is a good idea.

Why would they?

Stanford is private. UC is public and not particularly well run.

Would Harvard want to become part of the U. of Massachusetts system?

Would Columbia or Cornell want to join the SUNY (State University of NY) system?

Would Princeton choose to disappear into Rutgers?

This wasn’t a “Why would they” question as much as a “has it happened” question.