  In the collinear twist-three approach, we calculate for the first time the
gluon contribution to double (longitudinal-transverse) spin asymmetry A_{LT}
for open charm production in proton-proton collisions measurable at RHIC.
Utilizing the Ward-Takahashi identity for the non-pole part of the hard
scattering amplitude, we derive a factorized, gauge invariant formula for the
asymmetry. The result may be combined with the previous studies of single-spin
asymmetry in the same channel and allows for a systematic analysis of
three-gluon correlations inside a transversely polarized nucleon.
