It is well known that the polarization of a linearly polarized (LP) light would rotate after passing through a single layer graphene under the bias of a perpendicular magnetostatic field. Here we show that a corresponding phase shift could be expected for circularly polarized (CP) light, which can be engineered to design the circular polarization sensitive devices. We theoretically validate that an ultrathin graphene-based absorber with the thickness about lambda/76 can be obtained, which shows efficient absorption >90% within incident angles of +/- 80 degrees. The angle-independent phase shift produced by the graphene is responsible for the nearly omnidirectional absorber. Furthermore, a broadband absorber in frequencies ranging from 2.343 to 5.885 THz with absorption over 90% is designed by engineering the dispersion of graphene.