We investigate the absorption of a spin current at a ferromagnetic-metal/Pt-oxide interface by measuring current-induced ferromagnetic resonance. The spin absorption was characterized by the magnetic damping of the heterostructure. We show that the magnetic damping of a Ni$_{81}$Fe$_{19}$ film is clearly enhanced by attaching Pt-oxide on the Ni$_{81}$Fe$_{19}$ film. The damping enhancement is disappeared by inserting an ultrathin Cu layer between the Ni$_{81}$Fe$_{19}$ and Pt-oxide layers. These results demonstrate an essential role of the direct contact between the Ni$_{81}$Fe$_{19}$ and Pt-oxide to induce sizable interface spin-orbit coupling. Furthermore, the spin-absorption parameter of the Ni$_{81}$Fe$_{19}$/Pt-oxide interface is comparable to that of intensively studied heterostructures with strong spin-orbit coupling, such as an oxide interface, topological insulators, metallic junctions with Rashba spin-orbit coupling. This result illustrates strong spin-orbit coupling at the ferromagnetic-metal/Pt-oxide interface, providing an important piece of information for quantitative understanding the spin absorption and spin-charge conversion at the ferromagnetic-metal/metallic-oxide interface.