Recent studies in devices comprising metal antiferromagnets have demonstrated the feasibility of a novel spintronic concept in which spin-dependent phenomena are governed by an antiferromagnet instead of a ferromagnet. Here we report experimental observation of the anisotropic magnetoresistance in an antiferromagnetic semiconductor Sr2IrO4. Based on ab initio calculations, we associate the origin of the phenomenon with large anisotropies in the relativistic electronic structure. The antiferromagnet film is exchange coupled to a ferromagnet, which allows us to reorient the antiferromagnet spin-axis in applied magnetic fields via the exchange spring effect. We demonstrate that the semiconducting nature of our AFM electrode allows us to perform anisotropic magnetoresistance measurements in the current-perpendicular-to-plane geometry without introducing a tunnel barrier into the stack. Temperature-dependent measurements of the resistance and anisotropic magnetoresistance highlight the large, entangled tunabilities of the ordinary charge and spin-dependent transport in a spintronic device utilizing the antiferromagnet semiconductor.