I am a CA lawyer.  Yes, you have the right to make a claim against the drunk driver.  In fact, if the driver was arrested and is convicted of driving under the influence, you will be a stronger position.  If you have an injury, make sure that you are being treated by a doctor.  It is also advisable to take photographs of your car and any visible injuries on your body.  Finally, I recommend that you hire an attorney to represent you in this case.  Lawyers who handle personal injury cases, such as myself, handle these matters on a contingent fee basis.  What that means is that you will not have to pay the lawyer for the work being done until the case settles.  The lawyer charges a fee, typically 331/3%, of the personal injury recovery.  One more thing, my office, like most others, does not charge a fee to help negotiate any property damage repair or recovery.  Good luck.  Look on AttorneyPages.com for a lawyer in your area. 

Yes you can, in short. Read Mr. Klein's excellent explanation above

You should call me for a free consultation on your car accident case at 800-816-1529 x1. My law firm handles car accident cases all over the State of California. You can read about these types of on my website at www.thepersonalinjury.com . You may also email me directly at norman@norman-law.com .

I look forward to discussing this case with you.

Norman