One of the most fundamental forms of magnon-phonon interaction is an intrinsic property of magnetic materials, the magnetoelastic coupling. This particular form of interaction has been the basis for describing magnetic materials and their strain related applications, where strain induces changes of internal magnetic fields. Different from the magnetoelastic coupling, more than 40 years ago, it was proposed that surface acoustic waves may induce surface magnons via rotational motion of the lattice in anisotropic magnets. However, a signature of this magnon-phonon coupling mechanism, termed magneto-rotation coupling, has been elusive. Here, we report the first observation and theoretical framework of the magneto-rotation coupling in a perpendicularly anisotropic ultra-thin film Ta/CoFeB(1.6 nm)/MgO, which consequently induces nonreciprocal acoustic wave attenuation with a unprecedented ratio up to 100$%$ rectification at the theoretically predicted optimized condition. Our work not only experimentally demonstrates a fundamentally new path for investigating magnon-phonon coupling, but also justify the feasibility of the magneto-rotation coupling based application.