Two scenarios of possible ion heating due to finite amplitude parallel propagating Alfvén waves in the solar atmosphere are investigated using a one-dimensional test particle approach. (1) A finite amplitude Alfvén wave is instantly introduced into a plasma (or equivalently, new ions are instantly created). (2) New ions are constantly created. In both scenarios, ions will be picked up by the Alfvén wave. In case 1, the wave scatters ions in the transverse direction leading to a randomization (or heating) process. This process is complete when a phase shift of ±π in the ion gyrospeed is produced between particles with characteristic parallel thermal speed and particles with zero parallel speed. This corresponds to (k is the wavenumber, and is the ion thermal speed). A ring velocity distribution can be produced for a large wave amplitude. The process yields a mass-proportional heating in the transverse direction, a temperature anisotropy, and a bulk flow along the background magnetic field. In case 2, continuous ion creation represents a continuing phase shift in the ion gyrospeed leading to heating. New particles are picked up by the Alfvén wave within one ion gyroperiod. It is speculated that the mechanism may operate in the chromosphere and active regions where transient events may generate finite amplitude Alfvén waves.