  We show that an energy gap is induced in graphene by light-matter coupling to
a circularly polarized photon mode in a cavity. Using many-body perturbation
theory we compute the electronic spectra which exhibit photon-dressed sidebands
akin to Floquet sidebands for laser-driven materials. In contrast with Floquet
topological insulators, in which a strictly quantized Hall response is induced
by light only for off-resonant driving in the high-frequency limit, the
photon-dressed Dirac fermions in the cavity show a quantized Hall response
characterized by an integer Chern number. Specifically for graphene we predict
that a Hall conductance of $2 e^2/h$ can be induced in the low-temperature
limit.
