The bead-spring model is the fundamental model in the field of polymer physics, but its conformational dynamics under stress-controlled conditions had not been analyzed so far. For completeness of the model, this dynamics was recently analyzed for linear and star bead-spring chains during the creep process under a constant stress. In this paper, the analysis is extended to the bead-spring ring chain having no free end. Since all segments of the ring chain are equivalent (due to the lack of the chain end) and the orientational anisotropy summed over these segments corresponds to the stress (stress-optical rule), the segments have the same, time-independent anisotropy throughout the creep process. In other words, no retardation occurs for the segment anisotropy. However, the ring chain exhibits the retarded creep behavior (delay in achieving the steady flow state), as similar to the behavior of the linear chain. The analysis of the conformational dynamics reveals that this retardation of the ring corresponds to growth of the orientational correlation between different segments with time. The analysis also indicates a difference between the ring and linear chains that the ring segments have either positive or negative correlations depending on their separation along the chain backbone while the correlation is always positive for the segments of the linear chain.