In some states, if you live together for a certain amount of time, and hold yourself out as married, you can be legally considered married, without a marriage license or ceremony. Currently, only ten (10) states recognize common law marriage: Alabama, Colorado, Kansas, Rhode Island, South Carolina, Iowa, Montana, Oklahoma, Pennsylvania and Texas, and Washington D.C..
California is not on this list.  California does NOT have common law marriage.
However, if you are previously considered married in one of these common law states, and later move to California, California will recognize the previous common law marriage.