A long-lived quantum memory is a firm requirement for implementing a quantum repeater scheme. Recent progress in solid-state rare-earth-ion-doped systems justifies their status as very strong candidates for such systems. Nonetheless an optical memory based on spin-wave storage at the single-photon-level has not been shown in such a system to date, which is crucial for achieving the long storage times required for quantum repeaters. In this letter we show that it is possible to execute a complete atomic frequency comb (AFC) scheme, including spin-wave storage, with weak coherent pulses of $bar{n} = 2.5 pm 0.6$ photons per pulse. We discuss in detail the experimental steps required to obtain this result and demonstrate the coherence of a stored time-bin pulse. We show a noise level of $(7.1 pm 2.3)10^{-3}$ photons per mode during storage, this relatively low-noise level paves the way for future quantum optics experiments using spin-waves in rare-earth-doped crystals.