The actin cytoskeleton gives the cell shape and support, is crucial for cell locomotion, and participates in cell division. To study the mechanical properties of the actin cytoskeleton as modeled by rigidity percolation (disordered spring networks), we have analytically and numerically studied disordered spring networks with an underlying anisotropy, i.e. where the filaments are preferentially oriented along one direction. We found, for example, that the increasing the anisotropy, increases the filament density required for a nonzero shear modulus (rigidity).