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A magnetically tunable multi-band switchable frequency terahertz (THz) absorber based on graphene is proposed, and its absorption performance is analyzed using the 4 × 4 transfer matrix method. The results indicate that the proposed absorber achieves absorption amplitude tuning across multiple switchable THz frequencies by adjusting the static bias magnetic field. Moreover, both absorption and modulation depths exceed 90% for the left-handed circularly polarized wave. This performance can be attributed to the unequal Landau levels distribution of graphene in the quantum domain and the properties of photonic crystals, which include photonic bandgaps and optical localization. This study may have significant potential in various frequency-switchable components, such as circular polarization sensors, circular polarizers, and magnetic circular dichroism optical detectors. [ABSTRACT FROM AUTHOR]