Depending how far along you are in your period of probation, you can petition the court for an early termination of your probation, followed an expungement of the charges from your criminal record.
Do realize, however, that this will only affect a criminal records check. DMV will still have it in their records.
A P. C. 1203.4 petition is always a sound effort, as is an early termination of probation request. But realize that California's version of "expungement" is a weak substitute for any kind of erasure. The prior conviction is not deleted, erased, removed, or otherwise "expunged" from your criminal history. Instead, there is simply an additional notation made to the record, reflecting the fact of the order under P C. 1203.4. As you have already been advised, the DMV record, which is the most likely of your records to be viewable and of interest to potential employers, is unaffected. Furthermore, where the potential employer can discover the criminal history record, the prior offense will be discernible.
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You must be off probation to petition for expungement. If not, you must first petition for early termination of probation. You must have a good reason to get early termination. "I don't want potential employers to know I was convicted of DUI" is not likely to be a sufficient reason. However, if you can show other changed circumstances, you may be able to prevail. Consult an attorney
I agree with all the posters. I've handled expungements in Alameda County before and probation releases in Santa Clara County. If I can help, please feel free to get in touch.
The answer provided above is based upon California and/or New York law and is based solely upon the limited information provided by the poster. No attorney-client relationship is created. A future in-person consultation may reveal additional facts that may change the answer provided.