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Recent experiments on magic-angle twisted bilayer graphene have shown the formation of flat bands, suggesting that electronic correlation effects are likely to dominate in this material. However, a global transport measurement showing distinct signatures of strong correlations—such as local moments arising from the flat bands—is missing. Here we demonstrate the presence of emergent local moments through their impact on entropy extracted from thermopower measurements. In addition to sign changes in the thermopower at the Dirac point and full filling of the flat bands, we observe sign changes near the quarter-filled bands that do not vary with temperature from 5 K to 60 K. This is in contrast to temperature-dependent crossing points seen in our study on twisted bilayer graphene devices with weaker correlations. Furthermore, we find that applying a magnetic field reduces the thermopower, consistent with spin entropy suppression observed in layered oxides under partial spin polarization. Neither the robust crossing points nor the suppression by a magnetic field can be explained solely from the contributions of band fermions; instead, our data suggest a dominant contribution coming from the entropy of the emergent localized moments of a strongly correlated flat band.