Ionization of cometary neutral molecules produces ions which are picked up by the solar wind. The cometary ion pickup process for comet Giacobini-Zinner is studied in two ways: (1) with a test particle method in which trajectories are numerically calculated for several thousand ions whose initial locations were chosen randomly with probability proportional to the neutral density and (2) with a quasi-linear diffusion model. The cometary ion distribution function was calculated with the test particle model at several locations upstream of the bow shock and for several types of magnetic fluctuations (or waves). These waves were allowed to propagate in both directions along the magnetic field at the Alfven speed. Both pitch angle scattering and energy diffusion are evident in the derived ion distributions. The monochromatic waves result in less ion acceleration than turbulent fluctuations with about the same amplitude. The calculated ion distribution functions are in reasonable agreement with the distributions measured in the vicinity of comet Giacobini-Zinner in 1985 by particle detectors on the ICE spacecraft when the ratio of power in sunward propagating Alfven waves to the power in antisunward propagating waves is assumed to lie between about 20% and 50%. However, the quasi-linear diffusion model results agree best with the measured distribution functions when the power ratio is only about 3%. ¿ American Geophysical Union 1994