It depends whether your criminal record is a conviction for one of the crimes indicated in the Adam Walsh Act. http://www.ojp.usdoj.gov/smart/pdfs/practitioner_guide_awa.pdf
The first question is whether you are a U.S. citizen. If yes, you are eligible to petition on behalf of a spouse or fiance (not a girlfriend) assuming she has no impediment barring entry to the U.S.
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