  The center-of-mass position of a single trapped atomic ion is measured and
tracked in time with high precision. Employing a near-resonant radio frequency
field of wavelength 2.37 cm and a static magnetic field gradient of 19 T/m, the
spatial location of the ion is determined with an unprecedented
wavelength-relative resolution of 5 $\times$ 10$^{-9}$, corresponding to an
absolute precision of 0.12 nm. Measurements of an electrostatic force on a
single ion demonstrate a sensitivity of 2.2 $\times$ 10$^{-23}
~\text{N}/\sqrt{\text{Hz}}$. The real-time measurement of an atom's position
complements the well-established technique of scanning near-field radio
frequency transmission microscopy and opens up a novel route to using this
method with path breaking spatial and force resolution.
