α-moganite is a recently discovered polymorph of silica, commonly intergrown with quartz in natural microcrystalline silica samples. An important challenge is finding an effective method for estimating its amount in a sample under study, which is important for its applications, related to the technology of growth of dielectric layers, as well as for fundamental problems, related to the formation of both terrestrial and lunar mineral deposits and biogenic formation. One of these methods is vibrational spectroscopy, with the help of which the presence of a particular compound is determined by the presence of characteristic spectral lines. In this work, the search for such lines is carried out using density functional theory calculations and comparisons of the IR and Raman spectra of α-quartz and α-moganite. With the help of such calculations, the stability of the moganite structure has been proven for the first time, and its spectral characteristics have been determined over the entire range of vibrational frequencies. Several new spectral lines characteristic of α-moganite were discovered in the 65–85 cm−1 region. Moreover, the evolution of spectral peculiarities under hydrostatic pressure was studied.