The photon emission and absorption spectra of a plasma rotating with constant angular velocity Ω are derived in terms of the spectral function of the current–current correlator. In contrast to the non-rotating case, the leading contribution arises already at one-loop order. The photon emission spectrum and its elliptic flow are calculated for a rotating quark–gluon plasma and compared with the leading two-loop result for a non-rotating plasma. The rotating plasma is found to emit significantly more soft photons than the non-rotating one. An analysis of the emission and absorption of cylindrical waves indicates that photons with energy ω and azimuthal quantum number m satisfying ω < mΩ are emitted at a higher rate than they are absorbed, thereby exhibiting the phenomenon of superradiance. It is further argued that these superradiant modes induce an instability of the magnetic field that is generated concurrently with the plasma in relativistic heavy-ion collisions.