Toroidal rotation dynamics without any external torque sources in KSTAR Ohmic L-mode discharges is investigated. The KSTAR Ohmic plasmas mostly flow in the counter-current direction and the toroidal rotation velocity increases as the plasma density rises. The measured radial electric field in T-10 Ohmic plasmas is generally negative and its magnitude increases as the density rises [A. V. Melnikov et al., Nucl. Fusion 53, 093019 (2013)]. A theoretical picture is introduced in this study to explain how the radial electric field and the toroidal rotation change with the same tendency. The radial electric field can be built up to satisfy the ambipolarity condition and ultimately rotate the plasmas in the toroidal direction.