The thin-layer sectioning technique was used to determine the solute diffusivities of $^{198}\mathrm{Au}$ in single crystals of erbium. The results indicate a significant anisotropic diffusion behavior with the activation energy ${Q}_{\ensuremath{\parallel}} (\mathrm{parallel}\mathrm{to}\mathrm{the} c \mathrm{axis})=0.66\ifmmode\pm\else\textpm\fi{}0.015$ eV, and ${Q}_{\ensuremath{\perp}} (\mathrm{perpendicular}\mathrm{to}\mathrm{the} c \mathrm{axis})=1.03\ifmmode\pm\else\textpm\fi{}0.04$ eV. The results were interpreted in terms of an interstitial solute diffusion mechanism. Values of the migration energies, ${E}_{1i,\ensuremath{\parallel}}^{m}=0.501$ eV and ${E}_{1i,\ensuremath{\perp}}^{m}=0.871$ eV, associated with migration parallel and perpendicular to the $c$ axis, respectively, were evaluated using an anisotropic-elastic-continuum model. The analysis of the results allowed to determine the effective radius of the solvent atoms, nearest neighbors of an interstitial Au solute. This calculated value falls close to the value associated with the ionic radius of ${\mathrm{Er}}^{3+}$ for coordination number 8.