  We discuss the single transverse-spin asymmetry (SSA) to be observed in the
$D$-meson production with large transverse-momentum in semi-inclusive deep
inelastic scattering, $e p^\uparrow \rightarrow e D X$. 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. The complete
formula for the corresponding SSA in the leading-order QCD is expressed in
terms of the four independent gluonic correlation functions and reveals the
five independent structures with respect to the dependence on the azimuthal
angle for the produced $D$-meson. We present the numerical calculations of the
SSA formula at the kinematics relevant to a future Electron Ion Collider.
