Optical isolation enables nonreciprocal manipulations of light with broad applications in optical communications. Optical isolation by rotating structures has drawn considerable attention due to its magnetic-free nature and unprecedented performance. Conventional rotation-based optical isolation relies on the use of bulky cavities hindering applications in subwavelength photonics. Here, we propose a novel mechanism of optical isolation by integrating the unique dispersion of a hyperbolic metamaterial with the transverse spin-orbit interaction of evanescent waves. We show that rotation of a subwavelength hyperbolic nanoparticle breaks the time-reversal symmetry and yields two resonant chiral modes that selectively couple to the transverse spin of waveguide modes. Remarkably, the transverse spin-orbit interaction can give rise to unidirectional coupling and $>95%$ isolation of infrared light at an experimentally feasible rotation speed. Our work fuses the two important fields of optical isolation and photonic spin-orbit interactions, leading to magnetic-free yet compact nonreciprocal devices for novel applications in optical communications, chiral quantum optics, and topological photonics.