Can my employer in California fire me for any reason?

Whether or not your employer can fire you for any reason, or no reason at all, depends on whether or not you are an at-will employee. If you are an at-will employee, your employer can fire you for any reason except where it is unlawful. For example, they are not allowed to fire you due to your race, sex, religion, or disability. 

If, however, you signed a written employment contract, the employer may only be able to terminate your position based on the terms and conditions of the contract.

Again, as this is an area of law that can be state-specific, it is best to speak with an attorney if you believe you were illegally terminated.