The MicroBooNE detector is a liquid argon time projection chamber at Fermilab designed to study short-baseline neutrino oscillations and neutrino-argon interaction cross-section. Due to its location near the surface, a good understanding of cosmic muons as a source of backgrounds is of fundamental importance for the experiment. We present a method of using an external 0.5 m (L) x 0.5 m (W) muon counter stack, installed above the main detector, to determine the cosmic-ray reconstruction efficiency in MicroBooNE. Data are acquired with this external muon counter stack placed in three different positions, corresponding to cosmic rays intersecting different parts of the detector. The data reconstruction efficiency of tracks in the detector is found to be $\epsilon_{\mathrm{data}}=(97.1\pm0.1~(\mathrm{stat}) \pm 1.4~(\mathrm{sys}))\%$, in good agreement with the Monte Carlo reconstruction efficiency $\epsilon_{\mathrm{MC}} = (97.4\pm0.1)\%$. This analysis represents a small-scale demonstration of the method that can be used with future data coming from a recently installed cosmic-ray tagger system, which will be able to tag $\approx80\%$ of the cosmic rays passing through the MicroBooNE detector.