In this work we study the anomalous top quark-gluon couplings chromoelectric dipole moment and chromomagnetic dipole moment in a general two Higgs doublet model with $CP$ violation. We find that this model provides an important contribution from the ${Y}_{tt}$ Yukawa coupling that needs to be taken into account. The predictions for the chromomagnetic dipole moment and chromoelectric dipole moment obtained are $\ensuremath{-}0.03<\mathrm{\ensuremath{\Delta}}{\stackrel{\texttildelow{}}{k}}_{t}<\ensuremath{-}0.005$ and $|\mathrm{\ensuremath{\Delta}}{\stackrel{\texttildelow{}}{d}}_{t}|<0.005$, respectively.