Unsteady Reynolds-Averaged Navier-Stokes (RANS) simulations are performed on a full-scale marine propeller to obtain its torsional added mass and damping coefficients under various hydrodynamics conditions. These coefficients, also called propeller coefficients, originate from additional hydrodynamic forces and moments acting on the propeller in a non-uniform hull wakefield and are vital for torsional vibration calculations. A CFD model in the propeller open water test (OWT) condition is used in this paper for a full-scale propeller to obtain these coefficients. The effect of a nonuniform wakefield is numerically modeled by superimposing a torsional motion with a uniform flow, and the torsional vibration is numerically modeled by superimposing a harmonic torsional oscillation on the propeller’s rotation motion in the propeller OWT condition. The propeller’s resultant added mass and damping coefficients are computed and compared with available methods, such as Archer and Schwanecke. The influence of excitation frequency, advance ratio, and vibration magnitude on added mass and damping coefficients is studied. Moreover, the effect of the propeller’s geometrical properties such as the pitch ratio, expanded area ratio, blade skew, and blade number on the propeller’s coefficients are investigated.