Muon accelerators offer an attractive option for a range of future particle physics experiments. They can enable high energy (TeV+) high energy lepton colliders whilst mitigating the difficulty of synchrotron losses, and can provide intense beams of neutrinos for fundamental physics experiments investigating the physics of flavor. The method of production of muon beams results in high beam emittance which must be reduced for efficient acceleration. Conventional emittance control schemes take too long, given the very short (2.2 microsecond) rest lifetime of the muon. Ionisation cooling offers a much faster approach to reducing particle emittance, and the international MICE collaboration aims to demonstrate this technique for the first time. This paper will present the MICE RF system and its role in the context of the overall experiment.