In this paper, an augmented continuum mechanics is applied to investigate the size dependent pull-in instability of torsional nano-electromechanical actuator considering the coupling effect between torsion and bending. A set of dimensionless governing equations of the system is derived using the effective size dependent flexural and torsional rigidity of the actuator. The governing equations are solved using implicit function theorem. The static instability parameters i.e pull-in angle, pull-in displacement and pull-in voltage are computed as a function of bending/torsion coupling ratio as well as the actuator geometrical characteristics and size effect parameter. It is found that pull-in characteristics computed by the augmented continuum mechanics has a considerable difference with those predicted via classical theory when the dimensions of the nano-actuator are of the order of the internal material length scale parameter.