The answer depends in part on where in CA the property is located. Some cities and/or counties have rent control laws that limit the increase of rent. Whether the tenant is on a lease or a term rental agreement is also a factor. Whether the tenant is on a lease or a term rental agreement is also a factor. This is a complex issue, and you might want to contact a lawyer if you're uncertain. However, having said that:
If the property is under rent control, get a copy of the rent control regulations. A list of cities with rent control laws can be found at www.caltenantlaw.com
If not under rent control, and tenant is on a lease, then rent can not be increased during the term of the lease unless the lease explicitly allows increases. If the tenant is on a month-to-month (or other term) rental agreement, you can raise the rent unless the agreement specifies that you cannot.
If you are allowed to raise the rent, either through a lease that specifies increases or a term agreement that does not prohibit them, on a non rent-controlled property, then the amount generally is not limited by law. You could raise rent to $1 million a day, if you wish, though unfair raises might be met with suits citing other causes, like discrimination, so be reasonable).
State law requires you to give at least 30 days notice of any increase up to 10%, and 60 days notice if the increase exceeds 10% (Note: That is 10% total over a 12 month period, so if you raise it 4% today and 4% next month, you would have to give 60 days notice to raise it more than an additional 2% within the following 10 months). Notice must be in writing, and allow an additional 5 days if served by mail.
The California Dept. Of Consumer Affairs has some basic rent law information at:
www.dca.ca.gov

Hope this help...