  We discuss the single transverse-spin asymmetry (SSA) to be observed in the
$D$-meson production with large transverse-momentum in semi-inclusive DIS
(SIDIS), $e p^\uparrow \rightarrow e D X$. This contribution is embodied as a
twist-3 mechanism in the collinear factorization, which is induced by purely
gluonic correlation inside the transversely-polarized nucleon, in particular,
by the three-gluon correlation effects. We derive the first complete formula
for the corresponding SSA in the leading-order QCD, revealing the five
independent structures with respect to the dependence on the azimuthal angle
for the produced $D$-meson. Our result obeys universal structure behind the
SSAs in a variety of hard processes. We present the numerical calculations of
our SSA formula for the $D$-meson production at the kinematics relevant to a
future Electron Ion Collider.
