The search for and study of exotic quantum states in novel low-dimensional quantum materials have triggered extensive research in recent years. Here, we systematically study the electronic and magnetic structures in the newly discovered two-dimensional quantum material C₃N within the framework of density functional theory. The calculations demonstrate that C₃N is an indirect-band semiconductor with an energy gap of 0.38 eV, which is in good agreement with experimental observations. Interestingly, we find van Hove singularities located at energies near the Fermi level, which is half that of graphene. Thus, the Fermi energy easily approaches that of the singularities, driving the system to ferromagnetism, under charge carrier injection, such as electric field gating or hydrogen doping. These findings not only demonstrate that the emergence of magnetism stems from the itinerant electron mechanism rather than the effects of local magnetic impurities, but also open a new avenue to designing field-effect transistor devices for possible realization of an insulator–ferromagnet transition by tuning an external electric field.