The distribution of chemical elements in primitive meteorites (chondrites), as building blocks of terrestrial planets, provides insight into the formation and early differentiation of Earth. The processes that resulted in the depletion of some elements [such as chromium (Cr)] in the bulk silicate Earth relative to chondrites, however, remain debated between leading candidate causes: volatility versus core partitioning. We show through high-precision measurements of Cr stable isotopes in a range of meteorites, which deviate by up to ~0.4 per mil from those of the bulk silicate Earth, that Cr depletion resulted from its partitioning into Earth's core, with a preferential enrichment in light isotopes. Ab initio calculations suggest that the isotopic signature was established at mid-mantle magma ocean depth as Earth accreted planetary embryos and progressively became more oxidized.