Spin-orbit torques (SOT) in thin film heterostructures originate from strong spin-orbit interactions (SOI) that, in the bulk, generate a spin current as the result of extrinsic spin-dependent, skew or/and side-jump, scattering, or in the intrinsic case due to Berry curvature in the conduction band. While most SOT studies have focused on materials with heavy metal components, the oxide perovskite SrRuO3 has been predicted to have a pronounced Berry curvature. Through quantification of its spin current by the SOT exerted on an adjacent Co ferromagnetic layer, we determine that SrRuO3 has a strongly temperature (T) dependent spin Hall conductivity which becomes particularly high at low T, e.g. sigma_{SH} geqslant (hbar/2e)3x10^{5} Omega^{-1}m^{-1} at 60 K. Below the SrRuO3 ferromagnetic transition, non-standard SOT components develop associated with the magnetic characteristics of the oxide, but these do not dominate as with spin currents from a conventional ferromagnet. Our results establish a new approach for the study of SOI in epitaxial conducting oxide heterostructures and confirm SrRuO3 as a promising candidate material for achieving new and enhanced spintronics functionalities.