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ANSWER: Unfortunately, yes, it can be a problem. Under the Adam Walsh Act, your criminal history can affect your eligibility to sponsor your girlfriend for immigrant benefits.
Before you can sponsor her, you will first have to overcome your history by getting a "no risk" waiver from the USCIS. To do that, you have to show that you pose no risk of harm to the foreign family member, beyond a reasonable doubt. That is not easy to do. I highly recommend that you find a lawyer who specializes in these types of cases help you.
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