We develop a theoretical framework for Landau levels in quasiperiodic twisted bilayer graphene at a ${30}^{\circ }$ twist angle, a system without translational symmetry but possessing 12-fold rotational symmetry. Using a quasiband formalism, we incorporate the magnetic field through a conventional momentum substitution in the zero-field Hamiltonian. This approach provides a transparent physical interpretation by directly relating the Landau levels to the quasiband structure, allowing them to be understood as quantized orbits of quasiband pockets. By using this method, we reveal distinctive spectral features, including nearly flat bands with weak magnetic-field dependence and highly degenerate levels arising from 12 off-center pockets. The resulting Landau levels are classified by two quantum numbers: the Landau-level index and the angular momentum associated with the underlying quasicrystalline symmetry. We also compute the magneto-optical conductivity and show that optical transitions follow angular-momentum selection rules enforced by the 12-fold symmetry. Our approach provides a symmetry-based and computationally efficient framework for bulk quantum magneto-optics in quasicrystalline van der Waals systems, predicting spectroscopic signatures accessible in high-field infrared and THz experiments.

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• Electronic structure
• Landau levels
• Magneto-optical effect
• Twistronics
• Twisted bilayer graphene
• Tight-binding model