An equation for the neoclassical poloidal plasma rotation in tokamaks, which applies to ion cyclotron resonant heating (ICRH), has been obtained in an earlier work [Phys. Plasmas 8, 4390 (2001)]. The present work is devoted to a detailed study of the properties of an additional contribution arising from the non-Maxwellian part of the ion distribution. In a first approach, the effect of a temperature anisotropy is modeled by the use of a bi-Maxwellian equilibrium distribution function. In a second approach, the effect of the high energy ion tail is analyzed using the solution of a Fokker-Planck equation valid when ICRH fundamental heating is used. In both cases, a poloidal rotation speed larger than the poloidal ion sonic speed is expected at levels of ICRH power commonly encountered in tokamak experiments. (C) 2002 American Institute of Physics.