Our current understanding of Earth's core formation is limited by the fact that this profound event is far removed from us physically and temporally. The composition of the iron metal in the core was a result of the conditions of its formation, which has important implications for our planet's geochemical evolution and physical history. We present experimental and theoretical evidence for the effect of pressure on iron isotopic composition, which we found to vary according to the alloy tested (FeO, FeHx, or Fe3C versus pure Fe). These results suggest that hydrogen or carbon is not the major light-element component in the core. The pressure dependence of iron isotopic composition provides an independent constraint on Earth's core composition.