We report the observation of the intrinsic dampinglike spin-orbit torque (SOT) arising from the Berry curvature in metallic-magnet/CuO_{x} heterostructures. We show that a robust dampinglike SOT, an order of magnitude larger than a fieldlike SOT, is generated in the heterostructure despite the absence of the bulk spin-orbit effect in the CuO_{x} layer. Furthermore, by tuning the interfacial oxidation level, we demonstrate that the fieldlike SOT changes drastically and even switches its sign, which originates from oxygen-modulated spin-dependent disorder. These results provide important information for a fundamental understanding of the physics of the SOTs.