The present paper focuses on the effect of microcracks on the overall properties of viscoelastic materials. For this goal we extend Maxwell homogenization scheme to the case of viscoelasticity and derive explicit formulas for components of the anisotropic creep operator in dependence on scatter parameter characterizing orientation distribution of cracks. Microcracks can have any orientation distribution with randomly oriented and strictly parallel being the limiting cases. Viscoelastic behavior is described using fraction-exponential operators. The results are illustrated on example of microckracked polymethylmethacrylate (PMMA).