The electrical switching of magnetization through spin-orbit torque (SOT) 1 holds promise for application in information technologies, such as low-power, non-volatile magnetic memory. Materials with strong spin-orbit coupling, such as heavy metals(2-4) and topological insulators(5,6), can convert a charge current into a spin current. The spin current can then execute a transfer torque on the magnetization of a neighbouring magnetic layer, usually a ferromagnetic metal like CoFeB, and reverse its magnetization. Here, we combine a ferromagnetic transition metal oxide(7) with an oxide with strong spin-orbit coupling(8) to demonstrate all-oxide SOT devices. We show current-induced magnetization switching in SrIrO3/SrRuO3 bilayer structures. By controlling the magnetocrystalline anisotropy of SrRuO3 on (001)- and (110)-oriented SrTiO3 (STO) substrates, we designed two types of SOT switching schemes. For the bilayer on the STO(001) substrate, a magnetic-field-free switching was achieved, which remained undisturbed even when the external magnetic field reached 100 mT. The charge-to-spin conversion efficiency for the bilayer on the STO(110) substrate ranged from 0.58 to 0.86, depending on the directionality of the current flow with respect to the crystalline symmetry. All-oxide SOT structures may help to realize field-free switching through a magnetocrystalline anisotropy design.