I could find no such prohibition for a DUI. The closet I found was a section of the law that lists several factors which preclude issuance of a license including, but not limited to, being a habitual drunkard or abuser of controlled substances. I also found a section which states that persons convicted of drunk driving three times within a five-year period may possess but may not purchase a firearm. Looks like you should be able to get licensed.
To be sure you could check with an attorney that practices in PA.
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