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We study the problem of coupling partially coherent radially polarized (PCRP) vortex beams into a single-mode optical fiber. Using the well-known concept of the cross-spectral density (CSD) matrix, we derive a general expression for the coupling efficiency of the partially coherent beam into a single-mode fiber. We adopt PCRP vortex beams for incident beams and use our general results to discuss the effects of the coherence, topological charge, and wavelength on the coupling efficiency of an optical beam focused onto a single-mode fiber with a lens. Our results should be useful for any application that requires coupling of partially coherent beams into optical fibers.