The radioactive element astatine exists only in trace amounts in nature. Its properties can therfore only be explored by study of the minute quantitities artificially produced isotopes or by performing theoretical calculations. One of the most important properties influencing the chemical behaviour is the energy required to remove one electron from the valence shell, referred to as the ionization potenetial. Here we use laser spectroscopy to probe the optical spectrum of astatine near the ionization treshold. The observed series of Rydberg states enabled the first determination of the ionization potential of the astatine atom, 9.31751(8) eV. New ab initio calculations are performed to support the experimental result. The measured value serves as a benchmark for quantum chemistry calculations of the properties of astatine as well as for the teoretical prediction of the ionization potential of superheavy element 117, the heaviest homologue of astatine.