The eccentric RHS (rectangular hollow sections) joint offers improved mechanical properties and better space utilization. Its use in frame structures has gained significant attention. Currently, the initial rotational stiffness of RHS joints, the simplified finite element analysis method of eccentric RHS joints, and the influence of the spatial effect of RHS joints are still unknown. The purpose of this research is to establish a calculation formula for the initial rotational stiffness of eccentric RHS joints, study the influence of the spatial effect under complex stress conditions, and propose a mathematical model that can be used to simplify the analysis of eccentric RHS joints. The research findings indicate that the web plate’s deformation stiffness primarily influences the joints’ initial rotational stiffness. This increases with a higher beam-to-column depth-to-width ratio, beam-to-column thickness ratio, and column width-to-thickness ratio. The form of the moment distribution in the joint changes, and begins to have a significant effect on the rotational stiffness when the beam-to-column flange width ratio reaches and exceeds 0.7. The stiffeners have a direct additive effect on the joint stiffness. The influence of adjacent beams on the joint is minimal, and the spatial effect of the joint can be disregarded. Furthermore, the finite element analysis confirmed the accuracy of the power function model in accurately simulating the static load behavior of the joint, particularly the bending moment–angle relationship.