Collective excitations such as plasmons and paramagnons are fingerprints of atomic-scale Coulomb and exchange interactions between conduction electrons in metals. The strength and range of these interactions, which are encoded in the excitations’ dispersion relations, are of primary interest in research on the origin of collective instabilities such as superconductivity and magnetism in quantum materials. Here we report resonant inelastic x-ray scattering experiments on the correlated 4d-electron metal Sr2RhO4, which reveal a spin-orbit entangled collective excitation. The dispersion relation of this mode is opposite to those of antiferromagnetic insulators such as Sr2IrO4, where the spin-orbit excitons are dressed by magnons. The presence of propagating spin-orbit excitons implies that the spin-orbit coupling in Sr2RhO4 is unquenched, and that collective instabilities in 4d-electron metals and superconductors must be described in terms of spin-orbit entangled electronic states.