The interaction between the chiral light and matter is vital to construct on-chip multi-functional photonic circuits. The well-known spin-orbit interaction has obtained significant attention in manipulation of light with different circular polarization states. We propose a robust Y-type surface plasmon nano-waveguide structure to effectively sort spin-dependent photons. The optimized simulation results demonstrated that the waveguide modes excited by circularly polarized light with different spin states can be selectively coupled to one of two branching waveguides, with a unidirectionality efficiency up to 0.95. This research may open up new ways for the on-chip implementation of complex photonic functions, nano-photonic circuits, and nano-optical manipulation.