The terahertz (THz) absorption properties of a gated graphene monolayer placed on top of a one-dimensional photonic crystal is investigated in the presence of a perpendicular magnetostatic bias. The response of electrons to the magnetic field is inspected in the quantum regime, due to the low doping level of graphene grown on the C-terminated surface of silicon-carbide. It has been shown that there is the possibility of achieving enhanced absorption at low magnetic fields for certain states of circular polarization of light. Furthermore, adjusting the gate voltage of the graphene provides another method of tuning absorption in the proposed structure. Therefore, one can obtain enhanced absorption with the appropriate choices of magnetic and electric biases. We believe that these properties make our structure suitable for designing tunable graphene-based THz absorbers.