Lord Kelvin with his discovery of the anisotropic magnetoresistance (AMR) phenomenon in Ni and Fe was 70 years ahead of the formulation of relativistic quantum mechanics the effect stems from, and almost one and a half century ahead of spintronics whose first commercial applications relied on the AMR. Despite the long history and importance in magnetic sensing and memory technologies, the microscopic understanding of the AMR has struggled to go far beyond the basic notion of a relativistic magnetotransport phenomenon arising from combined effects on diffusing carriers of spin-orbit coupling and broken symmetry of a metallic ferromagnet. Our work demonstrates that even this seemingly generic notion of the AMR phenomenon needs revisiting as we observe the ohmic AMR effect in a nano-scale film of an antiferromagnetic (AFM) semiconductor Sr2IrO4 (SIO). Our work opens the recently proposed path for integrating semiconducting and spintronic technologies in AFMs. SIO is a particularly favorable material for exploring this path since its semiconducting nature is entangled with the AFM order and strong spin-orbit coupling. For the observation of the low-field Ohmic AMR in SIO we prepared an epitaxial heterostructure comprising a nano-scale SIO film on top of an epilayer of a FM metal La2/3Sr1/3MnO3 (LSMO). This allows the magnetic field control of the orientation of AFM spins in SIO via the exchange spring effect at the FM-AFM interface.