Strong light-matter interactions within nanoscale structures offer the possibility of optically controlling material properties. Motivated by the recent discovery of intrinsic long-range magnetic order in two-dimensional materials, which allows for the creation of novel magnetic devices of unprecedented small size, we predict that light can couple with magnetism and efficiently tune magnetic orders of monolayer ruthenium trichloride (RuCl3). First-principles calculations show that both free carriers and optically excited electron-hole pairs can switch monolayer RuCl3 from the proximate spin-liquid phase to a stable ferromagnetic phase. Specifically, a moderate electron-hole pair density (on the order of 10^13 cm-2) can significantly stabilize the ferromagnetic phase by 10 meV/f.u. in comparison to the zigzag phase, so that the predicted ferromagnetism can be driven by optical pumping experiments. Analysis shows that this magnetic phase transition is driven by a combined effect of doping-induced lattice strain and itinerant ferromagnetism. According to the Ising-model calculation, we find that the Curie temperature of the ferromagnetic phase can be increased significantly by raising carrier or electron-hole pair density. This enhanced opto-magnetic effect opens new opportunities to manipulate two-dimensional magnetism through non-contact, optical approaches.