Constrained friction processing (CFP) is a novel technique for producing fine-grained rods from lightweight materials such as aluminum and magnesium alloys. In this process, a rotating shoulder is plunged into the base material, extruding it into the shoulder’s cavity while being constrained by the rotating probe. The resulting shear forces and heat generation induce metallurgical transformations, such as dynamic recrystallization, promoting grain refinement. Magnesium rods processed by CFP exhibit a characteristic ultrastrong texture because of the anisotropy of the hexagonal close-packed structure. In this study, the material flow during CFP of AM50 was analyzed based on local texture variations along the rod, determined using electron backscatter diffraction. The resulting mechanical behavior was evaluated using Vickers micro hardness and quasi-static tensile tests on samples taken from two positions along the rod. The results show a strong dependence of local mechanical properties on the texture and anisotropy of the processed material. Significant improvements in ductility were observed, especially in the outer regions of the rod along the plunging direction, showing an elongation at break determined at 47%. This highlights the critical role of CFP-induced texture in determining mechanical properties and indicate the possibility of texture tailoring achieved by the control of critical process parameters that rules the material flow.