The optical Hall effect manifests itself as angular momentum separation induced by the photonic spin-orbit interaction. Such a celebrated Hall effect, at the mercy of the angular momentum conservation law, has attracted tremendous interest owing to its science and potential applications in precision measurements, material characterizations, and photonic devices, as well as quantum optics. However, to date, the Hall effect only expresses angular momentum separation of the spin term (spin-spin separation) or the orbital term (orbit-orbit separation), whereas the spin-orbit angular momentum separation, named as the spin-orbit Hall effect, remains unexplored. Here we demonstrate for the first time that this spin-orbit effect could appear when the polarization state of the light beam evolves adiabatically from the equator toward the poles of the higher-order Poincaré sphere, rather than the conventional Poincaré sphere. In this scenario, the intrinsic spin and orbital components of the light beam become separated, leading to equal nonzero spin and orbital angular momenta in magnitude but with the opposite sign. We further show that the spin-orbit Hall effect can be controlled via crystal birefringence and hence holds promise for applications; e.g., it is shown that the separated orbital angular momentum could be utilized in particle manipulations.