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 scattering 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 \times 10 ^ { 12 } G. The 3–79 keV luminosity of the system during the two epochs assuming a nominal distance of 50 kpc was 3.667 \pm 0.007 \times 10 ^ { 38 } \mathrm { erg s ^ { -1 } } and 3.983 \pm 0.007 \times 10 ^ { 38 } \mathrm { erg s ^ { -1 } } . Both values are much higher than the critical luminosity of \approx 1.5 \times 10 ^ { 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 ( \sigma \approx 0.45 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 .