We experimentally demonstrate that when two spin-orbit coupled orbital angular momentum (OAM) modes of opposite topological charge co-propagate in the Kerr nonlinear regime in a hollow ring-core optical fiber, the vectorial mode superposition exhibits a unique power-dependent rotation effect. This effect is analogous to nonlinear polarization rotation in single-mode fibers, however, the added spatial dimension produces a visually observable rotation of the spatial pattern emerging from the fiber when imaged through a linear polarizer. A dielectric metasurface q-plate was designed and fabricated to excite the desired mode combination in a hollow ring-core fiber that supports stable propagation of OAM modes. The observed spatial patterns show strong agreement with numerical simulations of the vector coupled nonlinear Schrödinger equations. These results constitute the first measurements of what can be described as the spin-orbit coupled generalization of the nonlinear polarization rotation effect.