  We describe a novel method to measure the surface charge densities on optical
fibers placed in the vicinity of a trapped ion, where the ion itself acts as
the probe. Surface charges distort the trapping potential, and when the fibers
are displaced, the ion's equilibrium position and secular motional frequencies
are altered. We measure the latter quantities for different positions of the
fibers and compare these measurements to simulations in which unknown charge
densities on the fibers are adjustable parameters. Values ranging from $-10$ to
$+50$ e/$\mu$m$^2$ were determined. Our results will benefit the design and
simulation of miniaturized experimental systems combining ion traps and
integrated optics, for example, in the fields of quantum computation,
communication and metrology. Furthermore, our method can be applied to any
setup in which a dielectric element can be displaced relative to a trapped
charge-sensitive particle.
