It is occasionally possible to interpret strongly interacting many-body systems within a single-particle framework by introducing suitable fictitious entities, or 'quasi-particles'. A notable recent example of the successful application of such an approach is for a two-dimensional electron system that is exposed to a strong perpendicular magnetic field. The conduction properties of the system are governed by electron-electron interactions, which cause the fractional quantum Hall effect(1). Composite fermions, electrons that are dressed with magnetic flux quanta pointing opposite to the applied magnetic field, were identified as apposite quasi-particles that simplify our understanding of the fractional quantum Hall effect(2,3). They precess, like electrons, along circular cyclotron orbits, but with a diameter determined by a reduced effective magnetic field(4-10). The frequency of their cyclotron motion has hitherto remained enigmatic, as the effective mass is no longer related to the band mass of the original electrons and is entirely generated from electron-electron interactions. Here we demonstrate enhanced absorption of a microwave field in the composite fermion regime, and interpret it as a resonance with the frequency of their circular motion. From this inferred cyclotron resonance, we derive a composite fermion effective mass that varies from 0.7 to 1.2 times that of the electron mass in vacuum as their density is tuned from 0.6 x 10(11) cm(-2) to 1.2 x 10(11) cm(-2).