  We study the single-transverse spin asymmetry for open charm production in
the semi-inclusive lepton-hadron deep inelastic scattering. We calculate the
asymmetry in terms of the QCD collinear factorization approach for $D$ mesons
at high enough $P_{h\perp}$, and find that the asymmetry is proportional to the
twist-three tri-gluon correlation function in the proton. With a simple model
for the tri-gluon correlation function, we estimate the asymmetry for both
COMPASS and eRHIC kinematics, and discuss the possibilities of extracting the
tri-gluon correlation function in these experiments.
