The effects of the fusion born α particles on the stability of the RWM are numerically investigated for one of the advanced steady state scenarios in ITER. The α contribution is found to be generally stabilizing, compared with the thermal particle kinetic contribution alone. The same conclusion is achieved following both a perturbative and self-consistent approach. The latter generally predicts less stabilization than the former. At high enough plasma pressure, the self-consistent approach predicts two unstable branches for the ITER plasma studied here. The stabilizing effect from α particles is found to be generally weak, in particular in terms of the modification of the stability boundary. The effect is more pronounced only at fast enough plasma rotation frequency, roughly matching the α precession frequency, which is in the order of a few per cent of the toroidal Alfvén frequency for ITER. A simple, energy principle based, fishbone-like dispersion relation is proposed to gain a qualitative understanding of the numerical results.