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The extrusion process (EP) consists of heat and mechanical treatments under different conditions of moisture, shear, and pressure and rapidly causes structural alterations and changes in the functional properties of the extruded material. The aim of this study was to evaluate the effect of extrusion conditions and optimize the wheat bran extrusion conditions to achieve the greatest content of phenolic compounds and antioxidant activity using response surface methodology. The EP factors evaluated were feed moisture (FM) (25–33.54%) and final extrusion temperature (T) (140–180 °C). The properties evaluated in the extruded material were bound total phenol content (BTPC), total phenolic compounds and antioxidant activity (AOX). Analysis of variance (ANOVA) and response surface methodology were used in the evaluation. The determination coefficients, (FM)2 and (T)2, very significantly affected the BTPC and bound 2,2-diphenyl-1-picrylhydrazyl content (BDPPHC). The optimization was performed by overlaying two contour plots to predict the best combination regions. The optimized extrusion conditions were the following: FM = 30% and T = 140 °C, which provided BTPC = 3547.01 μgGAE/g (predicted: 3589.3 μgGAE/g) and BDPPHC = 9.5 μmolTE/g (predicted: 10.4 μmolTE/g); and FM = 30% and T = 180 °C, which provided BTPC = 3342.3 μgGAE/g (predicted: 3727.7 μgGAE/g) and BDPPHC = 9.5 μmolTE/g (predicted: 9.3 μmolTE/g). The EP increased the phenolic compounds and AOX, and enhancement of these properties in wheat bran products could make them functional foods.