The enhancement of heat transfer in circular tubes using twisted tape inserts has attracted significant attention from the research community. Using twisted tape in heat exchangers contributes to higher heat transfer efficiency. In this study, a new type of twisted tape with ring inserts has been proposed and simulated. A validated numerical model was developed and solved using ANSYS Fluent and Response Surface Methodology (RSM) optimization and statistical tools. The tested design factors include Reynolds number (Re) (5000–20,000), twist pitch (50–150 mm), insert width (18–24 mm), and insert length (250–500 mm), which are used to generate a 31-point design runs via RSM. The responses for these 31 runs are evaluated using the validated computational fluid dynamic model. Three different responses were assessed for every run, including the Nusselt number (Nu), the ratio of the Nusselt number to that of a smooth pipe (Nu/Nuo), and the ratio of pressure drop to that of a smooth pipe (DP/DPo). The results show that the most significant factor affecting Nu is the Reynolds number, followed by the pitch of the twisted tape. Both the Nu/Nuo and DP/DPo ratios are significantly affected by the insert length and pitch, respectively. The results revealed that the Re and the twist pitch significantly influence the enhancing heat transfer characteristics of the proposed twisted tape insert.