That depends ... what was the criminal charge for which you were convicted? How long ago was it? And how old were you at the time?
Assuming the conviction was for misdemeanor DUI per CVC 23152(a) or (b) then such a conviction is NOT an automatic bar to employment. However, as it shows a serious lack of good judgment, it will hamper the applicant's ability to get a job in law enforcement - especially in these days of tight budgets and laid off and experienced applicants looking for jobs.
Some agencies may have an absolute bar to employing people convicted of DUI, but that would be a policy or practice and not a legal requirement. Most agencies will look at the incident in context. As part of the background they will obtain a copy of the report and review it for the applicant's actions. They will evaluate the employee's history before and since that time. if the incident was some time in the past, say, 5 years old or more, and the applicant had maintained steady employment and/or gone to school, stayed out of trouble, and had no perceived problem with alcohol since that time, the applicant may find fertile ground to land on. But, if the applicant still parties and drinks like a fish, has held a new job every 6 months, and is characterized as a "party animal" by his or her friends, maybe another career would be in order.
As a note, I conduct law enforcement pre-employment background investigations and have done so for 9 years.