The short answer is yes. In California employment is considered to be “at will” which means that you can be fired at any time with or without cause. There are some exceptions to this general rule, however. You cannot be fired based on a discriminatory reason. For example, you cannot be fired based on your age (over 40) or your religion, or because you have a physical disability or because of your gender or sexual orientation or because you are a member of certain other protected statuses.
You also cannot be fired for asking to be paid your earned wages or for other reasons such as taking medical leave if you qualify under the Family Medical Leave Act for job protection.