  The electron spin is a promising qubit candidate for quantum computation and
quantum information. Here we propose and analyze a mechanically-induced single
electron spin resonance, which amounts to a rotation of the spin about the
$x$-axis in a suspended carbon nanotube. The effect is based on the coupling
between the spin and the mechanical degree of freedom due to the intrinsic
curvature-induced spin-orbit coupling. A rotation about the $z$-axis is
obtained by the off-resonant external electric driving field. Arbitrary-angle
rotations of the single electron spin about any axis in the $x$-$z$ plane can
be obtained with a single operation by varying the frequency and the strength
of the external electric driving field. With multiple steps combining the
rotations about the $x$- and $z$-axes, arbitrary-angle rotations about
arbitrary axes can be constructed, which implies that any single-qubit gate of
the electron spin qubit can be performed. We simulate the system numerically
using a master equation with realistic parameters.
