We study theoretically the combined effect of the spin-orbit and Zeeman interactions on the tunneling electron transport through a single-channel quantum ring threaded by magnetic flux. We focus on the high temperature case (temperature is much higher than the level spacing in the ring) and demonstrate that spin-interference effects are not suppressed by thermal averaging. In the absence of the Zeeman coupling the high-temperature tunneling conductance of the ring exhibits two types of oscillations: Aharonov-Bohm oscillations with magnetic flux and AharonovCasher oscillations with the strength of the spin-orbit interaction. For weak tunneling coupling both oscillations have the form of sharp periodic antiresonances. In the vicinity of the antiresonances the tunneling electrons acquire spin polarization, so that the ring serves as a spin polarizer. We also demonstrate that the Zeeman coupling leads to appearance of two additional peaks both in the tunneling conductance and in the spin polarization.