RF design of a crab cavity (2π/3, 11.9942 GHz) for the Compact Linear Collide (CLIC) is presented. As part of the UK-CLIC collaboration, CERN is building two copper prototypes, designed by Lancaster University / Cockcroft Institute. The first prototype to be made will be a 12 cell undamped cavity and the second will be waveguide damped cavity. The RF test at CERN will help characterisation of the dipole mode with X-band RF pulses of 15 MW peak power and pulse length of ∼ 242 ns. Since the cavity frequency and phase advance per cell are identical to those of the CLIC main linac, the first prototype could exploit CERN's X-band cavity characterisation facilities. A fully damped cavity will be required for the actual machine in order to meet the luminosity specs. The damped prototype will use an identical coupler type as the undamped one, but the cells will have damping waveguides with / without dielectric material.