We propose nonreciprocal phonon lasing in a coupled cavity system composed of an optomechanical resonator and a spinning resonator. We show that the optical Sagnac effect leads to significant modifications in both the mechanical gain and the power threshold for phonon lasing. More importantly, the phonon lasing in this system is unidirectional; that is, the phonon lasing occurs when the coupled system is driven in one direction but not the other. Our work establishes the potential of spinning optomechanical devices for low-power mechanical isolation and unidirectional amplification. This provides a new route, well within the reach of current experimental abilities, to operate cavity optomechanical devices for a wide range of applications such as directional phonon switches, invisible sound sensing, and topological or chiral acoustics.