The miniaturization of magnetic devices toward the limit of single atoms calls for appropriate tools to study their magnetic properties. We demonstrate the ability to measure magnetization curves of individual magnetic atoms adsorbed on a nonmagnetic metallic substrate with use of a scanning tunneling microscope with a spin-polarized tip. We can map out low-energy magnetic interactions on the atomic scale as evidenced by the oscillating indirect exchange between a Co adatom and a nanowire on Pt(111). These results are important for the understanding of variations that are found in the magnetic properties of apparently identical adatoms because of different local environments.