In two-dimensional (2D) hyperbolic materials, energy is directed into their deep subwavelength polaritonic modes through four narrow beams. Hyperbolic whispering-gallery mode nanocavity-confined phonon polaritons (PhPs) display a strongly enhanced light-matter interaction in the infrared regime. Particularly, the unidirectional phonon-polarization excitation in nanocavities has a potential application value in an on-chip integrated optical circuit design, efficient optical sensors, and enhanced spectral technology. Here, we explore the hyperbolic whispering-gallery mode PhPs on the cross section of a hexagonal BN nanotube (BNNT) and demonstrate that efficient unidirectional excitation can be achieved using a circularly polarized electric dipole, combining with optical spin-orbit coupling. Our results demonstrated that the undirectionality of the hyperbolic polariton propagation in a nanocavity can be conveniently achieved, independent of the structure symmetry of the nanocavity, providing potential applications in nanoscale light propagation, on-chip optical devices, and communication.