We report the detection of an exoplanet candidate in orbit around ${sigma}$ Persei from a radial velocity (RV) survey. The system exhibits periodic RV variations of $579.8{pm}2.4$ days. The purpose of the survey is to search for low-amplitude and long-period RV variations in giants and examine the origin of the variations using the fiber-fed Bohyunsan Observatory Echelle Spectrograph installed at the 1.8-m telescope of Bohyunsan Optical Astronomy Observatory in Korea. We present high-accuracy RV measurements of ${sigma}$ Per made from December 2003 to January 2014. We argue that the RV variations are not related to the surface inhomogeneities but instead a Keplerian motion of the planetary companion is the most likely explanation. Assuming a stellar mass of $2.25{pm}0.5$ $M_{odot}$, we obtain a minimum planetary companion mass of $6.5{pm}1.0$ $M_{Jup}$, with an orbital semi-major axis of $1.8{pm}0.1$ AU, and an eccentricity of $0.3{pm}0.1$ around ${sigma}$ Per.