Magnons are collective precessional excitations of electron spins and are ubiquitous in emerging information technologies. Here, we show that the crystal lattice can support an analogous precessional mode of phonon angular momentum. Superposition of a circularly polarized phonon and a linearly polarized phonon normal to the circular-motion plane generates a transverse angular-momentum component that rotates at their difference frequency and decays on a timescale set by the participating phonon linewidths, defining a mode with its own resonance and lifetime. Coupling between spin and phonon angular momentum hybridizes this precessional mode with a magnon near resonance. Our results establish phonon angular momentum precessional modes as lattice analogues of magnons and identify their spectroscopic and time-domain signatures.