We explore crystal nucleation kinetics in suspensions containing particles experiencing short-range anisotropic interactions. A kinetic model is developed where cluster growth is written in terms of the rates of single particle aggregation onto and dissociation from cluster surfaces. Aggregation rates are determined for particles interacting with centrosymmetric interactions and corrected to account for the low probability of bond formation due to orientational constraints. The rates of dissociation are determined as the sum of the independent rates of bond breakage via translational and rotational diffusion of particles on cluster surfaces. The resulting nucleation rates display remarkable sensitivity to the degree of anisotropy. Under identical supersaturations and average strengths of interaction, slight changes in the degree of anisotropy result in several tens of orders of magnitude changes in nucleation rates. Surprisingly, crystal nucleation rates can either increase or decrease depending on how the degree of anisotropy is altered. These studies are discussed in terms of what is known about the equilibrium thermodynamics and kinetics of crystal nucleation in protein solutions.