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Mutual lattice orientations dictate the types and magnitudes of forces between crystalline particles. When lattice polarizability is anisotropic, the van der Waals dispersion attraction can, in principle, contribute to this direction dependence. We report measurement of this attraction between rutile nanocrystals, as a function of their mutual orientation and surface hydration extent. At tens of nanometers of separation, the attraction is weak and shows no dependence on azimuthal alignment or surface hydration. At separations of approximately one hydration layer, the attraction is strongly dependent on azimuthal alignment and systematically decreases as intervening water density increases. Measured forces closely agree with predictions from Lifshitz theory and show that dispersion forces can generate a torque between particles interacting in solution and between grains in materials.