SrIrO3 is a correlated semimetal with narrow t2g d-bands of strong mixed orbital character resulting from the interplay of the spin-orbit interaction due to heavy iridium atoms and the band folding induced by the lattice structure. In ultrathin layers, inversion symmetry breaking, occurring naturally due to the presence of the substrate, opens new orbital hopping channels, which in presence of spin-orbit interaction causes deep modifications in the electronic structure. Here, we show that in SrIrO3 ultrathin films the effect of inversion symmetry breaking on the band structure can be externally manipulated in a field effect experiment. We further prove that the electric field toggles the system reversibly between a metallic and an insulating state with canted antiferromagnetism and an emergent anomalous Hall effect. This is achieved through the spin-orbit driven coupling of the electric field generated in an ionic liquid gate to the electronic structure, where the electric field controls the band structure rather than the usual band filling, thereby enabling electrical control of the effective role of electron correlations. The externally tunable antiferromagnetic insulator, rooted in the strong spin-orbit interaction of iridium, may inspire interesting applications in spintronics. © 2023, The Author(s).