We report the first experimental observation of a steady-state, microwave-driven inverse Faraday effect in a high-temperature superconductor. Circularly polarized microwave radiation generates a helicity-dependent response in an epitaxial YBa₂Cu₃O_(7-δ) film, detected using homodyne Hall transport. The optomagnetic response emerges exclusively below T_c, vanishes in the normal state, and exhibits no power-dependent counterpart under linearly polarized excitation. The effective optomagnetic conversion reaches 1.75 T/(W cm⁻²), surpassing optical benchmarks by several orders of magnitude. At higher microwave powers, the signal collapses when the self-generated field exceeds B_c1, marking the onset of a vortex phase-slip regime, and subsequently re-emerges at mode-locked vortex-washboard harmonics. These results establish steady-state microwave optomagnetism as a route to contactless, non-inductive magnetic control and nonequilibrium vortex spectroscopy in superconducting quantum systems.