and form entangled states. The properties of these collective excitations, such as polaritons of light and phonons in semiconductors, can combine the benefits of each subsystem. In the emerging field of quantum information control, a promising direction is provided by the combination between long-lived atomic states and the accessible electrical degrees of freedom in superconducting cavities and qubits. Here we demonstrate the possibility to integrate circuit cavity quantum electrodynamics with phonons. Besides coupling to a microwave cavity, our superconducting transmon qubit interacts with a resonant phonon mode in a micromechanical resonator, allowing the combination of long lifetime, strong tunable coupling, and ease of access. We measure the phonon Stark shift, as well as the splitting of the transmon qubit spectral line into motional sidebands representing transitions between electromechanical polaritons formed by phonons and the qubit. In the time domain, we observe coherent sideband Rabi oscillations between the qubit states and phonons. This advance may allow for storage of quantum information in long-lived phonon states, and for investigations of strongly coupled quantum systems near the classical limit.