  Both the parallel residual stress and parallel turbulent acceleration driven
by electrostatic collisionsless trapped electron mode (CTEM) turbulence are
calculated analytically using gyrokinetic theory. Quasilinear results show that
the parallel residual stress contributes an outward flux of co-current rotation
for normal magnetic shear and turbulence intensity profile increasing outward.
This may induce intrinsic counter-current rotation or flattening of the
co-current rotation profile. The parallel turbulent acceleration driven by CTEM
turbulence vanishes, due to the absence of a phase shift between density
fluctuation and ion pressure fluctuation. This is different from the case of
ion temperature gradient (ITG) turbulence, for which the turbulent acceleration
can provide co-current drive for normal magnetic shear and turbulence intensity
profile increasing outward. Its order of magnitude is predicted to be the same
as that of the divergence of the residual stress [Lu Wang and P.H. Diamond,
Phys. Rev. Lett. {\bf 110}, 265006 (2013)]. A possible connection of these
theoretical results to experimental observations of electron cyclotron heating
effects on toroidal rotation is discussed.
