The toroidal rotation of a plasma with alpha particles is studied. The various mechanisms and factors of alpha-particle influence on rotation are considered: (a) the difference between the actual radial profile shape of the alpha particles and the profile shape of alpha-particle production; (b) the finite relaxation times of the toroidal angular momentum for the various components of a fusion plasma; and (c) the non-zero average longitudinal velocity of alpha particles escaping from a plasma. The alpha-particle longitudinal current in the peripheral region of an International Thermonuclear Experimental Reactor-like tokamak is found, using the assumption that the alpha-particle radial distribution is determined by the diffusion of the toroidally trapped particles.