Technically speaking, by CA law:
If you are planning on claiming CA as your state of residence, you have 10 days to register your vehicle upon taking action to be a CA resident. These are things like: getting a CA driver's license, registering to vote, getting a job, renting a place of residence - the overall picture of these actions demonstrate that you want to make CA your permanent home.
If you plan on keeping WA residency while attending school in CA, then you shouldn't need to register your vehicle in CA, as long as you don't get a CA license and/or register to vote here, and keep your permanent physical residence in WA - the indication here is that you are only living in CA to attend school and will be leaving after graduation. In this case you'll have to keep your vehicle up to code for your state of residence (inspections or what not) and have a valid license even while attending school here in CA as a non-resident.