Canadians Starting Business in USA
When registering a business in the U.S., you are not required to have U.S. citizenship. You may register a company without having to provide a social security number or U.S. address, and you are not required to submit any financial or identification documents.
We have a research article titled 'U.S. Companies for Foreigners' which explains the registration process and requirements, and also compares some of the top-recommended states and guides you to the online applications.
If you are going to be conducting business in California it's possible that is the state you would need to be registered in. Without knowing the exact nature of your business, it's hard to properly assess your situation and options.
You would need to consult a licensed immigration attorney regarding visa or U.S. citizenship procedures.