Transfer of angular momentum from helicity-controlled laser fields to a nonmagnetic electronic system can lead to the creation of magnetization. The underlying mechanism in metallic nanoparticles has been studied using different theoretical approaches. However, an understanding of the dynamics using an orbital-based quantum-mechanical method within the many-body theoretical framework is still due. To this end, the real-time formulation of time-dependent, density-functional theory is used to study induced orbital magnetism in metallic nanoparticles (clusters) excited by circularly polarized light. The nanoparticles are described by a spherical jellium model on a real-space grid. The polarized laser field gives rise to an angular momentum and, hence, a magnetic moment, which is maximum at the surface plasmon frequency of the nanoparticle, revealing that this is a resonant plasmonic effect. The primary contribution to the magnetic moment comes from surface currents generated by the plasmonic field, although some bulk contributions due to the quantum-mechanical nature of the system (Friedel oscillations) still persist. We compare several nanoparticles of K, Na, and Au having the same size and excited at their respective plasmon frequencies and show that the generated magnetic moment per energy pumped into the system is maximum for K and minimum for Au. A similar trend is observed for nanoparticles of the same chemical species but different sizes.