Local manipulation of electric fields at the atomic scale may enable new methods for quantum transport and creates new opportunities for field control of ferromagnetism and spin-based quantum information processing in semiconductors. We used a scanning tunneling microscope to position charged arsenic (As) vacancies in the gallium arsenide 110 [GaAs(110)] surface with atomic precision, thereby tuning the local electrostatic field experienced by single manganese (Mn) acceptors. The effects of this field are quantified by measuring the shift of an acceptor state within the band gap of GaAs. Experiments with varying tip-induced band-bending conditions suggest a large binding energy for surface-layer Mn, which is reduced by direct Coulomb repulsion when the As vacancy is moved nearby.