It can only be granted where there is a lack of "substantial evidence" as to one or more elements of the offense. Put another way, there has to be something so lacking that no reasonable jury could conclude, beyond a reasonable doubt, that the something existed. Example: one element is that you are driving. Let's say that the officers testify that you were NOT driving the vehicle when they encountered you, but that you were simply standing next to it. They offer no evidence as to whether...
Insufficiency of the evidence is a valid basis for reversal on appeal. But for the evidence to be insufficient, it has to be truly missing. The Court of Appeal uses a standard called "substantial evidence" which means, in reality, enough that a reasonable jury could have found it to be true. In order to be insufficient, it has to be unreasonably little such that no reasonable jury could find the allegation true.
It is not a crime of moral turpitude nor an aggravated felony, so it would fall into the "minor crime" exception. However, as the other attorney suggested, get a good DUI / criminal defense lawyer in Los Angeles and consult an immigration attorney.
You have to look at the terms of your probation. You were given a document at the time you were sentenced. That has the conditions. If you lost it, contact your lawyer to obtain a copy. Failing that, go to the court clerk and ask for a copy.
Most likely, there won't be a condition prohibiting it. But you HAVE to look. Anything you agreed to could be included as a probation condition.