Individual Fe atoms on a Cu(2)N/Cu(100) surface exhibit strong magnetic anisotropy due to the crystal field. We show that we can controllably enhance or reduce this anisotropy by adjusting the relative position of a second nearby Fe atom, with atomic precision, in a low-temperature scanning tunneling microscope. Local inelastic electron tunneling spectroscopy, combined with a qualitative first-principles model, reveal that the change in uniaxial anisotropy is driven by local strain due to the presence of the second Fe atom.