Reinforced concrete (RC) structural members such as spandrel, flanged and curved beams, slab beams, and bridge girders may be subjected to significant torsional loading. Despite extensive research on the strengthening of RC members, very little is known about the torsional behavior of RC members strengthened with fiber-reinforced polymer (FRP) sheets. Therefore, very limited guidelines apply to the design of externally bonded FRP systems for torsional strengthening, and no design provisions exist for the U-wrapped and 2-sided strengthening systems in torsion. This study aims to contribute to this growing area of research by developing a new analytical model to predict the full torsional response of strengthened RC members with many conventional configurations such as spiral, transverse and longitudinal FRP, continuous and intermittent strips along the beam length, side bonded, and full-wrapped systems. Moreover, this study provided an analytical model accurately predicting the contribution, efficiency, and failure mode of side-bonded strengthening systems. Additionally, the influence of various parameters such as FRP stiffness and transverse steel reinforcement ratio is taken into account in the constitutive law of concrete and internal reinforcement for the first time. The good agreement between the test results of 32 collected FRP-strengthened RC beams from the literature and the theoretical ones, which were predicted through programming proves the validity and accuracy of the presented theory.