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In most existing theories of metal cutting, the workpiece is assumed to be homogeneous and most continuum theories do not take into account the effect of crystallographic anisotropy, which causes the anisotropy of surface roughness. In single-point diamond turning, the depth of cut is small and cutting is usually performed within individual grains and the machined surface finish is significantly affected by the crystallographic orientation of the workpiece materials. In this paper, an experimental investigation was conducted to study the effect of rolling texture on the anisotropy of surface roughness in the single-point diamond turning of polycrystalline aluminum. Various textures in metals and alloys were prepared by a rolling and annealing treatment. A series of cutting tests were conducted under various depths of cut. The experimental results indicate that straight-rolled polycrystalline aluminum possesses a higher degree of roughness anisotropy than the cross-rolled variety. The effect of roughness anisotropy is found to decrease as the depth of cut increases. The findings provide an important means for improving surface quality in the diamond turning of polycrystalline materials.