Results of investigation on the transport of vorticity in Rivlin-Ericksen viscoelastic fluid in the presence of suspended magnetic particles is presented here. Equations governing the transport of vorticity in Rivlin-Ericksen viscoelastic fluid in the presence of suspended magnetic particles are obtained from the equations of magnetic fluid flow. From these equations it follows that the transport of solid vorticity is coupled with the transport of fluid vorticity. Further, we find that because of thermokinetic process, fluid vorticity may exist in the absence of solid vorticity, but when fluid vorticity is zero, then solid vorticity is necessarily zero. A two-dimensional case is also studied and found that the fluid vorticity is indirectly influenced by the temperature and the magnetic field gradient.