You can apply for a California id at the Department of Motor Vehicles (DMV) but it takes several weeks for processing. So it only makes sense if you are here for at least 3 months.
What to bring:
Your documents and your student id card, money to purchase the id
Pick your location. The Hillcrest DMV is closest, located at 3960 Normal St.
You can make an appointment online: http://www.dmv.ca.gov/dl/dl_info.htm#idcard
OR just go and wait in a very long line.
How to get to the Hillcrest DMV:
Walk to 5TH AVE at ELM ST
At 04:19 PM take the MTS BUS route 120 Fashion Valley Limited Stops
Get off the stop on 5TH AVE at UNIVERSITY AV at approximately 04:29 PM
At 04:35 PM take the MTS BUS route 10 University & College Limited Stops via University Ave
Get off the stop on UNIVERSITY AVE at RICHMOND ST at approximately 04:41 PM
walk North East to 3960 NORMAL ST
The clerk will ask you what you need: You need a California id
Side note:
*If you want to drive in San Diego, you need an international driver's license and you need to visit the DMV!