The rotation of the polarization of light after passing a medium in a magnetic field, discovered by Faraday, is an optical analogue of the Hall effect, which combines sensitivity to the carrier type with access to a broad energy range. Up to now the thinnest structures showing the Faraday rotation were several-nanometre-thick two-dimensional electron gases. As the rotation angle is proportional to the distance travelled by the light, an intriguing issue is the scale of this effect in two-dimensional atomic crystals or films—the ultimately thin objects in condensed matter physics. Here we demonstrate that a single atomic layer of carbon—graphene—turns the polarization by several degrees in modest magnetic fields. Such a strong rotation is due to the resonances originating from the cyclotron effect in the classical regime and the inter-Landau-level transitions in the quantum regime. Combined with the possibility of ambipolar doping3, this opens pathways to use graphene in fast tunable ultrathin infrared magneto-optical devices.