We present spectral and timing analysis of NuSTAR observations of RX J0520.5$-$6932 in the 3-79 keV band collected during its outburst in January 2014. The target was observed on two epochs and we report the detection of a cyclotron resonant scatteri
ng feature with central energies of $E_mathrm{CRSF} = 31.3_{-0.7}^{+0.8}$ keV and $31.5_{-0.6}^{+0.7}$ keV during the two observations, respectively, corresponding to a magnetic field of $B approx 2 times10^{12}$ G. The 3-79 keV luminosity of the system during the two epochs assuming a nominal distance of 50 kpc was $3.667pm0.007times 10^{38},mathrm{erg,s^{-1}}$ and $3.983pm0.007times10^{38},mathrm{erg,s^{-1}}$. Both values are much higher than the critical luminosity of $approx1.5times10^{37},mathrm{erg,s^{-1}}$ above which a radiation dominated shock front may be expected. This adds a new object to the sparse set of three systems that have a cyclotron line observed at luminosities in excess of $10^{38},mathrm{erg,s^{-1}}$. A broad ($sigmaapprox0.45$ keV) Fe emission line is observed in the spectrum at a central energy of $6.58_{-0.05}^{+0.05}$ keV in both epochs. The pulse profile of the pulsar was observed to be highly asymmetric with a sharply rising and slowly falling profile of the primary peak. We also observed minor variations in the cyclotron line energy and width as a function of the rotation phase.% As in observations of other cyclotron absorption line sources, there is a small ($Deltaphilesssim0.1$) phase difference between the peak of the cyclotron energy variation and the peak of the flux variation.
