Based on the modified Snyder-Mitchell model the transmission of the optical vortex soliton that is produced by two collinear Laguerre-Gaussian solitons (CLGS) in strongly nonlocal nonlinear media is studied. Under certain condition, the profiles of the optical vortex solitons will rotate in transmiting with the beam width unvarying, which are named rotating vortex solitons, and can be explained by the Gouy phase in superposed light field. A few rotating vortex solitons are shown and the many-ring rotating vortex solitons are accessed in strongly nonlocal nonlinear media.