Sumac sorghum bran was incorporated into expanded corn-based extruded snacks and evaluated for its impact on physical properties and antioxidant capacity. To assess the effects of bran level (0%-30%), screw speed (150-300 rpm), and feed rate (9-25 kg/h) on extrudate physical and chemical qualities, a three-factor response surface methodology (RSM) was used. Expansion ratio (ER), total phenolic content (TPC), oxygen radical absorbance capacity (ORAC), and tannin content were quantified, alongside secondary responses including hardness, color, and crispiness. Increasing bran inclusion significantly reduced expansion and increased product density, while enhancing TPC and ORAC. Specific mechanical energy (SME), hardness, and phenolic release, with minimal effects on ORAC and water absorption index (WAI), were a result of changing screw speed and feed rates. Increasing bran levels resulted in increased tannin content that followed a quadratic trend. Desirability functions were used to identify 20% bran, 184 rpm screw speed, and 21.76 kg/h feed rate as optimal conditions, yielding an ER of 3.25, TPC of 4832 µg GAE/g, ORAC of 165 µmol TE/g, and moderate tannin content (1067 CE µg/g). The use of tannin-rich sorghum bran to produce antioxidant-rich extruded snacks while maintaining acceptable product quality is supported by these findings.