We report on the dynamic nuclear polarization of a single charge-tunable self-assembled InAs/GaAs quantum dot in a longitudinal magnetic field of $sim$0.2T. The hyperfine interaction between the optically oriented electron and nuclei spins leads to the polarization of the quantum dot nuclei measured by the Overhauser-shift of the singly-charged excitons ($X^{+}$ and $X^{-}$). When going from $X^{+}$ to $X^{-}$, we observe a reversal of this shift which reflects the average electron spin optically written down in the quantum dot either in the $X^{+}$ state or in the final state of $X^{-}$ recombination. We discuss a theoretical model which indicates an efficient depolarization mechanism for the nuclei limiting their polarization to ~10%.