Ab-initio quantum mechanical calculations show that several percent potassium (K) can be alloyed into iron (Fe) at high pressure, suggesting that K may have been incorporated into the Earth's iron-rich core. We find that substitutional incorporation of K into the high-pressure polymorph of Fe, hexagonal close packed (hcp) $varepsilon$-Fe, is energetically favored over the separate elements. The incorporation of potassium causes iron to expand with increasing K concentration, in agreement with high-pressure experiments. This alloying process is of potential importance to understanding the thermal state and history of Earth's deep interior, as radioactive decay of 40K (half-life ~1.25 billion years) in the core could be an important source of energy for the geodynamo and mantle dynamics.