This study is an attempt to analyze the torsion buckling of a structure consisting of a cylindrical sandwich shell with two isotropic face sheets that surround a magnetorheological fluid (MRF) core layer. In this analysis, the simply supported boundary conditions were considered for the edges of the face sheets and the core layer. The components of displacement were calculated using the first-order shear deformation theory (FSDT), and the governing equations were derived using Hamilton’s principle and were solved drawing upon the Galerkin method. The parameters of interest were magnetic field, buckling analysis, torsional buckling convergence, h/L ratio, ht/h ratio, and rt/L ratio. The equations obtained from MATLAB were verified using ABAQUS owing to the absence of any similar study in the existing literature. A good agreement was observed in terms of torsional buckling, indicating the robustness of the proposed structure. As smart sandwich structures are broadly used in robotics and aerospace, this structure can be a good choice thanks to its lightness (resulting from the thinness of the face sheets and hollowness) and strength and resistance (contributed by MRF core layer), which can be modified with the application of different magnetic fields.