Light carries spin angular momentum, which, in the free space, is aligned to the direction of propagation and leads to intriguing spin Hall phenomena at an interface. Recently, it was shown that a transverse-spin (T-spin) state could exist for surface waves at an interface or for bulk waves inside a judiciously engineered metamaterial, with the spin oriented perpendicular to the propagation direction. Here, we demonstrate the spin Hall effect for transversely spinning light—a T-spin–induced beam shift at the interface of a metamaterial. It is found that the beam shift takes place in the plane of incidence, in contrast to the well-known Imbert-Fedorov shifts. The observed T-spin–induced beam shift is of geometrodynamical nature, which can be rendered positive or negative controlled by the orientation of T-spin of the photons. The unconventional spin Hall effect of light found here provides a previously unexplored mechanism for manipulating light-matter interactions at interfaces.