The Rhodotron is a recirculating radiofrequency accelerator, dedicated to industrial irradiation, which delivers electrons in the 3-20 MeV energy range. This study aims at pointing out the advantages and limits of such a device in another application: the free-electron laser. The recirculation in a single coaxial cavity allows an important reduction of Joule losses, as compared to a linear structure. We optimize the shape of the cavity thanks to the method of boundary integral equations. Using various models of electron optics, we find out the focusing conditions within a low current and show that the intensity limit depends on the accelerating gradient. We design far-infrared free-electron lasers, according to the electrons` energy; about 10 A peak currents are required. As a result, the energy of the beam injected in the Rhodotron will have to be several hundred keV.