The first use of linear magnetic birefringence (optical Cotton-Mouton effect) to observe a magnetic resonance is reported. This allows us to make the first direct observation of resonant motion of a ferromagnetic vortex. This vortex is present in an easy-plane garnet film at the intersection of two 90°Néel walls. Agreement between the resonant frequencies and our theory confirms a previously proposed equation of vortex motion. © 1984 The American Physical Society.