We demonstrate a large enhancement in the interaction of light with graphene through coupling with localized modes in a photonic crystal nanocavity. Spectroscopic studies show that a single atomic layer of graphene reduces the cavity reflection by more than a factor of one hundred, while also sharply reducing the cavity quality factor. The strong interaction allows for cavity-enhanced Raman spectroscopy on subwavelength regions of a graphene sample. A coupled-mode theory model matches experimental observations and indicates significantly increased light absorption in the graphene layer. The coupled graphene-cavity system also enables precise measurements of graphene's complex refractive index.