We study the single transverse-spin asymmetry for the inclusive open-charm production in the pp-collision, p(up arrow)p -> DX, induced by the three-gluon correlation functions in the polarized nucleon. We derive the corresponding twist-3 cross section formula in the leading order with respect to the QCD coupling constant. As in the case of the semi-inclusive deep inelastic scattering, ep(up arrow)p -> eDX, our result differs from the previous result in the literature. We also derive a "master formula'' which expresses the twist-3 cross section in terms of the gg -> c (c) over bar hard scattering cross section. We present a model calculation of the asymmetry at the RHIC energy, demonstrating the sensitivity of the asymmetry on the form of the three-gluon correlation functions.