Micro/nano-components often exhibit size effects in micro-electro-mechanical systems. A twisting vibration model of micro circular shafts is established based on nonlocal elasticity theory in this paper. Concrete examples are presented for three kinds of boundary conditions. It is shown that nonlocal effects make natural frequency of the twisting vibration decrease in comparison with the results based on classical continuum mechanics, and the differences are much larger with a smaller external characteristic scale (radius of cross section of the circular shafts) or for higher mode frequency. Vibration frequency is lower and the nonlocal scale effects disappear with the increase of cross sectional radius. Vibration mode function and relative rotation are also observed, of which the former are consistent with those by classical continuum theory. A numerical example proves that lattice constant of material may be adopted as the internal characteristic scale in micro/nano-mechanics approximately.