We introduce a magnetic extension of the Hückel molecular orbital (HMO) method in which the effect of an external magnetic field is incorporated through the Peierls substitution. In this formulation, the \pi -electron Hamiltonian of a conjugated molecule becomes a complex-weighted hopping operator defined on the hydrogen-depleted molecular graph. Under the standard Hückel assumptions, this operator coincides with the Hermitian adjacency matrix of the graph, providing a physical realization of Hermitian adjacency operators within molecular electronic structure theory. The magnetic-HMO framework enables the calculation of flux-dependent electronic observables such as bond currents, ring currents, orbital magnetization, and orbital susceptibility directly from the spectrum of the magnetic adjacency matrix. Applications to polycyclic aromatic hydrocarbons show that the magnetic response of \pi -electron systems is strongly controlled by molecular topology. In particular, linearly fused systems exhibit regular flux-dependent oscillations in the orbital magnetization, whereas nonlinear and extended molecules display more complex spectral rearrangements associated with multiple conjugation pathways.