Seismic body waves that sample Earth's core are indispensable for studying the most remote regions of the planet. Traditional core phase studies rely on well-defined earthquake signals, which are spatially and temporally limited. We show that, by stacking ambient-noise cross-correlations between USArray seismometers, body wave phases reflected off the outer core (ScS), and twice refracted through the inner core (PKIKP2) can be clearly extracted. Temporal correlation between the amplitude of these core phases and global seismicity suggests that the signals originate from distant earthquakes and emerge due to array interferometry. Similar results from a seismic array in New Zealand demonstrate that our approach is applicable in other regions and with fewer station pairs. Extraction of core phases by interferometry can significantly improve the spatial sampling of the deep Earth because the technique can be applied anywhere broadband seismic arrays exist.