Higher Chern insulators host multiple dissipationless chiral edge states, one per unit of Chern number. We study the collective plasmon modes of these edge states at a domain wall between Chern numbers C and -C, using a semiclassical model with Coulomb interactions. The plasmon dispersion is linear at long wavelengths, with a velocity that increases linearly with C. As in conventional two-dimensional metals, the edge plasmon generates an elliptically polarized electric field that decays into the bulk and drives electrons in circular orbits, producing a static orbital magnetization (inverse Faraday effect). For topological edge plasmons, the magnetization has a nontrivial spatial profile set by two competing length scales: the finite extent of the edge states and the plasmon wavelength. At fixed edge-charge amplitude, it grows strongly with C. At the domain wall, it approaches a finite plateau at low frequency and decays as 1/ω² at high frequency. Its temperature dependence is nonmonotonic, with a maximum at an intermediate temperature. These results show how the Chern number controls plasmon-induced magnetization, in contrast to conventional edge plasmons.