Will American son be able to sponsor his UKc mother who has US warrant

[Eurogirl]

In 2001 1 was arrested for a DUI, but left the U.S. before my court date. so had an arrest warrant. I returned to the U.K. With my children. My children adults have moved to the U.S. I live and work in the U.K. And want to move back to the U.S.A. My son will be sponsoring me, but I have told him we need to find out first if this will be a problem to do because of the DUI. I have no other criminal record. could someone advise me please? Thank you.