We solved the equations of the Snyder-Mitchell model, which is a model describing the propagation of optical beams in nonlocal nonlinear media with strong nonlocality, in a rotating cylindrical coordinate system, and obtained a self-similar analytical solution of an optical vortex soliton. The result shows that the radial part of the solution is the product of the Whittaker and power function. The beam has a ring-shaped structure rotating around its core.