Yes, you can sue a drunk driver even if there was no DUI conviction. No conviction means the prosecution could not prove their case beyond and to the exclusion of all reasonable doubt. The standard in a civil case is less. Evidence that the drunk driver was intoxicated or impaired will be a decision for the civil judge to determine. If there is sufficient evidence that the at fault driver was impaired a civil judge should let the jury determine whether or not the drunk driver disregarded human life by driving impaired.