Grease ice is an agglomeration of disk-shaped ice crystals, named frazil ice, which forms in turbulent waters of the Polar Oceans and in rivers as well. It has been recognized that the property of grease ice that it damps surface gravity waves could be explained in terms of the effective viscosity of the ice slurry. This paper is devoted to the study of the dynamics of a suspension of disk-shaped particles in a gravity wave field. For dilute suspensions, depending on the strength and frequency of the external wave flow, two orientation regimes of the particles are predicted: a preferential orientation regime with the particles rotating in coherent fashion with the wave field, and a random orientation regime in which the particles oscillate around their initial orientation while diffusing under the effect of Brownian motion. For both motion regimes, the effective viscosity has been derived as a function of the wave frequency, wave amplitude and aspect ratio of the particles. Model predictions have been compared to wave attenuation data in frazil ice layers grown in wave tanks.