SrIrO3, the three-dimensional member of the Ruddlesden–Popper iridates, is a paramagnetic semimetal characterised by a the delicate interplay between spin–orbit coupling and Coulomb repulsion. In this work, we study the anisotropic magnetoresistance (AMR) of SrIrO3 thin films, which is closely linked to spin–orbit coupling and probes correlations between electronic transport, magnetic order and orbital states. We show that the low-temperature negative magnetoresistance is anisotropic with respect to the magnetic field orientation, and its angular dependence reveals the appearance of a fourfold symmetric component above a critical magnetic field. We show that this AMR component is of magnetocrystalline origin, and attribute the observed transition to a field-induced magnetic state in SrIrO3.