CA employment law, is it legal for a company to take a copy of my drivers license

It is a legal form of identity and if you will be driving for them they absolutely need proof that you can drive.
Now just suppose someone out there without your training is going around claiming to be you, and getting jobs that should be yours. Imagine that person gets into an accident and YOU are blamed for it, You will
be happy to know that you can now prove you are working for another company which has proof of your identity and has confirmed it and this will defend you. By the way, I am not making this up. Almost every year I have some driver in my office who is about to lose his license because someone else is walking around with his id and has racked up a ton of unpaid traffic tickets.