The time dependence of the anisotropy of fluorescence in the B850 ring of the purple bacterium Rhodopseudomonas acidophila is calculated using the reduced density matrix formalism. The influence of static and dynamic disorder is taken into account simultaneously. Extending earlier calculations within the Markovian Redfield theory (Chem. Phys. 2002, 275, 1), which were based on a perturbative treatment of the exciton-phonon coupling, the focus of the present work is on memory effects within the exciton dynamics. For this purpose two different ways of treating non-Markovian effects are discussed and compared in a simplified model of the B850 ring with equal intercenter couplings. In addition, the influence of possible elliptical deformations of the ring on the anisotropy of fluorescence is discussed.