We report point-contact measurements of anisotropic magnetoresistance (AMR) in a single crystal of antiferromagnetic Mott insulator Sr2IrO4. The point-contact technique is used here as a local probe of magnetotransport properties on the nanoscale. The measurements at liquid nitrogen temperature reveal negative magnetoresistances (up to 28%) for modest magnetic fields (250 mT) applied within the IrO2 a−b plane and electric currents flowing perpendicular to the plane. The angular dependence of magnetoresistance shows a crossover from fourfold to twofold symmetry in response to an increasing magnetic field with angular variations in resistance from 1% to 14%. We tentatively attribute the fourfold symmetry to the crystalline component of AMR and the field-induced transition to the effects of applied field on the canting of antiferromagnetic-coupled moments in Sr2IrO4. The observed AMR is very large compared to the crystalline AMRs in 3d transition metal alloys or oxides (0.1%–0.5%) and can be associated with the large spin-orbit interactions in this 5d oxide while the transition provides evidence of correlations between electronic transport, magnetic order, and orbital states. The finding of this work opens an entirely new avenue to not only gain a new insight into physics associated with spin-orbit coupling but also to better harness the power of spintronics in a more technically favorable fashion