We investigate charm hadron production in relativistic heavy ion collisions with the quark combination model. The ${p}_{T}$ dependencies of the charm baryon-to-meson ratios such as $\frac{{\ensuremath{\Lambda}}_{c}+{\overline{\ensuremath{\Lambda}}}_{c}}{{D}^{0}+{\overline{D}}^{0}}$, $\frac{{\ensuremath{\Lambda}}_{c}+{\overline{\ensuremath{\Lambda}}}_{c}}{{D}^{+}+{D}^{\ensuremath{-}}}$, and $\frac{{\ensuremath{\Lambda}}_{c}+{\overline{\ensuremath{\Lambda}}}_{c}}{{D}_{s}^{+}+{D}_{s}^{\ensuremath{-}}}$ in $\mathrm{Au}+\mathrm{Au}$ collisions at 200 GeV are obtained. The charm baryon enhancement in the intermediate ${p}_{T}$ range is very prominent, which, together with the strangeness enhancement, further affects the charm hadron ratios. The modified charm hadron ratios lead to a $~17%$ increase of the charm cross section given by PHENIX. The dependencies of the charm hadron ratios on energy, centrality, and other parameters are also investigated. Predictions of the charm hadron ratios for the upgrade of the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC) are presented.