  The excess of positrons in cosmic rays above $\sim$10 GeV has been a puzzle
since it was discovered. Possible interpretations of the excess have been
suggested, including acceleration in a local supernova remnant or annihilation
of dark matter particles. To discriminate between these scenarios, the positron
fraction must be measured at higher energies. One technique to perform this
measurement is using the Earth-Moon spectrometer: observing the deflection of
positron and electron moon shadows by the Earth's magnetic field. The
measurement has been attempted by previous imaging atmospheric Cherenkov
telescopes without success. The Cherenkov Telescope Array (CTA) will have
unprecedented sensitivity and background rejection that could make this
measurement successful for the first time. In addition, the possibility of
using silicon photomultipliers in some of the CTA telescopes could greatly
increase the feasibility of making observations near the moon. Estimates of the
capabilities of CTA to measure the positron fraction using simulated
observations of the moon shadow will be presented.
