Yeah, that's not a problem. Get one of Nolo Press's books on starting a business, and go to town.
Any citizen can incorporate a business in any US state. You will need a registered agent in the state you registered in. This must be a real office staffed 9-5 M-F. Usually you contract this out for $300-ish a year, but you can be your own registered agent if you have a street address you are at 90% of the time. The criterion is that if a process server tries 3 times to deliver you a legal notice, he must succeed.
You will find that government license fees and the cost of registered agents will be higher in California than in other states. As you research setting up a corporation or LLC, you will learn other advantages of choosing another state.
However, if you do business in California (pay employees; interact with customers), you will need a state license to do business in California. If you formed your business in California, that "comes with it". Otherwise your out-of-state business must register as a foreign business with the Secretary of State. This costs about the same as registering a domestic (CA) business.
You will also need a California Registered Agent. Registering a foreign business and licensing it into CA can get a bit burdensome, you have to compare that to the benefits of foreign corporations to see if it's worth it.