You should be able to get this bike registered for street use in California.
First of all, make sure that it still has the California emissions sticker which should be on the inside of the left side cover over the air filter. There are two phillips head screws that need to be removed to remove this cover. If DMV won't directly issue you a plate, there is a process called dual registration that you can use which results in both an on road registration and an off road green sticker registration. You may have to educate the DMV clerks on how to do this since it is not very common. I can dig up the sections of the DMV code that you will need. You will also need to get a brake and light inspection done to confirm that all the street required electrical stuff is in place and functioning.
It's been a few years since I have done this but I should be able to find all the information that you will need to do this.