The mechanism for fast-ion-induced toroidal plasma rotation in the absence of external momentum input reported in Perkins et al (Perkins F.W. et al 2001 Phys. Plasmas8 2181) is examined in detail, at the level of single particle orbits and their collisional evolution, with the aim at clarifying the physical processes involved. This mechanism may be a contributing factor to the toroidal plasma rotation observed during the injection of intense ion cyclotron resonance frequency (ICRF) waves in recent tokamak experiments. It is found that the pitch-angle scattering of fast-ion orbits is essential in order to spin the plasma toroidally in the co-current direction. This situation is applicable to high-density C-MOD plasmas with intense ICRF wave absorption on the low-field side. However, in tokamaks such as JET, where fast ions with energies in the MeV range are produced by ICRF, the pitch-angle scattering is less important and counter-rotation is more likely to occur. More significantly, sheared rotation induced by ICRF fast ions can contribute to the quenching of turbulent fluctuations and of triggering internal transport barriers.