Supercritical carbon dioxide (SCO2) Brayton cycle has been widely used as a substitute for traditional steam cycles. As one of the key components of power-dense turbomachines, dry gas seal (DGS) has been considered one of the most suitable dynamic seal options due to its superior sealing performance. In this paper, considering the installation errors and external disturbances of the shaft end seal in a 14 MW supercritical carbon dioxide turbine, a comprehensive numerical study was conducted on the seal static and rotordynamic characteristics for four dry gas seal designs with different coning displacements. To account for the real gas effect of SCO2, a table lookup program was used to obtain the physics properties of CO2 under supercritical conditions based on the database of the National Institute of Standards and Technology (NIST). A frequency-dependent rotordynamic coefficients stiffness damping model (KC model) for SCO2 DGS and the mesh deformation technique were adapted to analyze the rotordynamic performance of the designed DGS. Steady-state numerical results of leakage rate, opening force, and steady film stiffness were analyzed and compared under four coning displacements. Transient numerical results of rotordynamic force coefficients were analyzed and studied under four coning displacement ratios and 10 vibration frequencies. Results show that the increase in coning displacement causes a 20% rise in leakage rate and a 2.4% increase in opening force. The tilted seal ring results in a maximum 30%–84% variation of the dynamic stiffness and greatly influences the damping coefficient. From a comprehensive view, the tilt of the seal rings brings undesired influences on both the static and rotor dynamic performance of SCO2 DGS. The distortion of the seal rings due to installation errors and other disturbances should be avoided as far as possible in SCO2 DGSs.