Experimentally, we observe angular-momentum transfer in electron-phonon scattering, although it is commonly agreed that phonons transfer mostly linear momentum. Therefore, the incorporation of angular momentum to describe phonons is necessary already for simple semiconductors and bears significant implications for the formation of new quasiparticles in correlated functional materials. Separation of linear and angular-momentum transfer in electron-phonon scattering is achieved by highly selective excitations on the femtosecond time scale of resonant inelastic x-ray scattering.