Stars are massive resonators that may be used as gravitational-wave (GW) detectors with isotropic sensitivity. New insights on stellar physics are being made possible by asteroseismology, the study of stars by the observation of their natural oscillations. The continuous monitoring of oscillation modes in stars of different masses and sizes (e.g., as carried out by NASA's Kepler mission) opens the possibility of surveying the local Universe for GW radiation. Red-giant stars are of particular interest in this regard. Since the mean separation between red giants in open clusters is small (a few light years), this can in principle be used to look for the same GW imprint on the oscillation modes of different stars as a GW propagates across the cluster. Furthermore, the frequency range probed by oscillations in red giants complements the capabilities of the planned eLISA space interferometer. We propose asteroseismology of red giants as a novel approach in the search for gravitational waves.