Cops nabbed Tanner -- who's 34 in real life, but plays a high-school senior on the CW show -- when he surrendered to federal prosecutors early Thursday morning.
Tanner's character on "One Tree Hill" is a high-achieving basketball star nicknamed "Skills" who's also a notorious ladies man.
He allegedly transferred Social Security cards "knowingly and intentionally" as part of a fraud scheme, cops said.
Tanner also acted alongside Samuel L. Jackson in feel-good basketball flick "Coach Carter" and has appeared on TV shows like "Moesha" and "Sister, Sister."
He's set to be arraigned in Brooklyn Criminal Court on Tuesday.