Efficient on-chip manipulation of photon spin is of crucial importance in developing future integrated nanophotonics as is electron spin in spintronics. The unidirectionality induced by the interaction between spin and orbital angular momenta suffers low efficiency in classical macroscopic optics, while it can be highly enhanced on subwavelength scales with suitable architectures. Here we propose and demonstrate a spin-sorting achiral split-ring coupler to unidirectionally excite dielectric-loaded plasmonic modes in two independent waveguides. We found experimentally that the impinging light with different spin can be selectively directed into one of two branching plasmonic waveguides with a directionality contrast up to 15.1 dB. A circular-helicity-independent compact beam splitter is also realized demonstrating great potential in designing complex interconnect nanocircuits. The illustrated approach is believed to open new avenues for developing advanced optical functionalities with a flexible degree of freedom in manipulation of on-chip chirality within chiral optics.