The novel electronic state of the canted antiferromagnetic (AFM) insulator strontium iridate (Sr2IrO4) is well described by the spin–orbit‐entangled isospin Jeff = 1/2, but the role of isospin in transport phenomena remains poorly understood. In this study, antiferromagnet‐based spintronic functionality is demonstrated by combining the unique characteristics of the isospin state in Sr2IrO4. Based on magnetic and transport measurements, a large and highly anisotropic magnetoresistance (AMR) is obtained by manipulating the AFM isospin domains. First‐principles calculations suggest that electrons whose isospin directions are strongly coupled to the in‐plane net magnetic moment encounter an isospin mismatch when moving across the AFM domain boundaries, which generates a high resistance state. By rotating a magnetic field that aligns in‐plane net moments and removes domain boundaries, the macroscopically ordered isospins govern dynamic transport through the system, which leads to the extremely angle‐sensitive AMR. As this work establishes a link between isospins and magnetotransport in strongly spin–orbit‐coupled AFM Sr2IrO4, the peculiar AMR effect provides a beneficial foundation for fundamental and applied research on AFM spintronics.