We introduce a radially polarized partially coherent twisted beam based on the unified theory of coherence and polarization. We also derive expressions of this beam propagating in free space and examine the influence of twist factor and coherence of the source plane on its propagation properties. It is found that both twist factor and coherence of the source plane affect its average intensity, polarization, and coherence. Those results also show that the beam is rotating with beam propagation, and the beam's rotation is independent of coherence of the source plane.