Over the last century, the seismic behavior of reinforced concrete (RC) beam–column joints has drawn many researchers’ attention due to their complex stress state. Such joints should possess sufficient capacity and ductility to ensure integrity and safety when subjected to cyclic loading during seismic events. In the literature, while most studies have focused on the behavior of concentric beam–column joints, few studies investigated the response of eccentric beam–column joints, in which the beam’s centerline is offset from the centerline of the column. Recent earthquakes demonstrated severe damage in eccentric beam–column joints due to their brittle torsional behavior, which may threaten the ductility required for the overall structural performance. To investigate the effect of brittle failure on the strength, ductility, and stability of eccentric beam–column joints, nonlinear finite element (FE) models were developed and validated. The FE model was employed to study the effect of some geometric parameters on the global and local behaviors of beam–column joints, including the joint type (exterior and interior), the column aspect ratio, and the joint aspect ratio. The results show that the joint aspect ratio, which is the ratio of beam-to-column depth, has a predominant effect on the failure behavior of the joint. Additionally, the increase in column aspect ratio alters the failure mode from brittle joint shear failure to ductile beam-hinge, although there is an increase in the joint torsional moment. The current study also showed that interior joints exhibited a higher out-of-plane moment as well as more extensive column torsion cracks compared to exterior joints.