Winsor et al.  first derived the geodesic acoustic mode (GAM) to be an elec-trostatic perturbation, localized within a narrow radial region of the plasma. There is, however, recent experimental evidence that the GAM also has a magnetic component with poloidal mode number 𝑚 = 2, existing outside the GAM surface, and even outside the plasma. Such a signal in 𝛿𝐵𝜃, with angular dependence sin2𝜃, has been detected in JT-60U  and in TCV  (possibly in other machines too), and was predicted theoretically in  in a study of the global structure of the corresponding eigenmode within ideal MHD. The ideal MHD model is unable to resolve the detailed fine structure of the GAM, but unlike standard kinetic treatments, it does naturally include the combination of the effects of compressibility, full electromagnetic effects, and mode coupling due to toroidal or shaping geometry effects, which are required to show that the mode has a global structure , including a surrounding magnetic halo existing also outside the plasma. While the theory in  was developed for toroidally rotating plasmas with circular cross section, the present work extends the analysis in those papers to (static) plasmas with a non-circular cross section. Such an extension of the analysis shows that i) the major effect of plasma shaping on the GAM frequency within the ideal MHD model is a decreasing GAM frequency with elongation, and ii) a non-circular plasma cross section, as well as a finite aspect ratio, induces other Fourier components than 𝑚=2 in the magnetic halo surrounding the GAM surface.