In real finite-sized polycrystals, the background elastic properties are no longer deterministic. Consequently, the corresponding phase velocities and attenuation coefficients also become random. Recently, we showed that second-order statistics of polycrystals’ effective elastic modulus tensor and the phase velocities reveal microstructural information such as the mean and standard deviation of grain size. In this paper, we extend the results to the case of textured polycrystals. The analytical framework is valid for cubic equiaxed grains with arbitrary grain size distribution and crystallographic texture level. The variabilities the phase velocities are shown to be proportional to the anisotropy level of the single crystals multiplied by the product of the two lowest eigenvalues of the local stiffness tensor. The former is inversely proportional to material’s density.