For the torsion of nanotubes in nonlocal differential model, under uniform moment loading and linear moment loading along the nanotube as well as concentrated moment load at the free end, the solution is independent of scale parameter and chirality. While for nonlinear and sinusoidal moments, the solution depends on the scale and is independent of chirality. In this study, a new approach is applied using doublet mechanics (DM) where the governing equation are obtained using shell equilibrium equations and solved by angular displacement expansions with considering the scale parameter. With this approach, unlike the other methods, the effects of scale parameter and chirality are considered simultaneously. It is shown that angular displacement increases by increasing the scale parameter for different types of moment loading and boundary conditions. On the other hand, a Zigzag chirality has a lower torsional stiffness compared to an Armchair one. To validate the obtained result, the results of this work are compared with the nonlocal theory, integral nonlocal-finite element method (FEM) and molecular dynamics (MD) simulation results. Good agreement is observed specially with the two latter approaches.