Polarized fluorescence spectra were recorded in the vicinity of the Se and Br K edges on crystals of the selenated protein aldose reductase in complex with a brominated inhibitor molecule. The X-ray absorption, refraction and resonant scattering tensors as a function of X-ray energy were derived from these data. Substantial dichroism and anisotropy of resonant scattering were observed in these crystals. It is predicted that these effects are present in many resonant scattering experiments in macromolecular crystallography and are likely to affect the diffraction data. As a consequence, the anomalous phasing signal in single- or multi-wavelength anomalous diffraction experiments can be optimized simply by choosing a judicious orientation of the crystal with respect to the polarization direction of the incident X-ray beam. A simple procedure is presented to achieve this, prior to any knowledge about the selenium sites.