  We study the spectrum of a one-dimensional Kitaev chain placed in a microwave
cavity. In the off-resonant regime, the frequency shift of the cavity can be
used to identify the topological phase transition of the coupled system. In the
resonant regime, the topology of the system can be controlled via the microwave
cavity occupation and, moreover, for a large number of photons (classical
limit), the physics becomes similar to that of periodically-driven systems
(Floquet insulators). We also analyze numerically a finite chain and show the
existence of a degenerate subspace in the presence of the cavity that can be
interpreted as a \textit{Majorana polariton}.
