The effect of pressure on the structure and reorientational motion of molecules in orientationally disordered (OD) crystalline phase of cubane has been investigated in detail using variable shape molecular simulations in constant-pressure constant-temperature ensemble. Complete orientational ordering occurs at a pressure of 1.0 GPa and the OD phase transforms to an orientationally ordered phase at this pressure. The transition is associated with a kink in the variation of structural parameters such as cell parameters, unit-cell volume, and interaction energy. This transition is also associated with an anomaly in specific heat. Above this transition pressure, the structural quantities display only smaller changes with further increase in pressure. The structure of high-pressure orientationally ordered (HPOO) phase has been characterized using radial distribution functions and orientational distribution function. From detailed analysis of the structure of HPOO phase we conclude that it is isostructural with low-temperature orientationally ordered phase. The OD phase has four times larger compressibility than the HPOO phase