We present a detailed study of the electrical properties of the deep ${\mathrm{Fe}}^{2+/3+}$ acceptor in InP by deep-level transient spectroscopy. The Fe acceptor transition has been observed in electron and hole emission in $n$- and $p$-type InP. A study of the electron emission signature reveals an electric-field enhancement of the emission rate, which is best explained by a polarization potential model. At 300 K electron and hole capture cross sections of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ and $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}{\mathrm{cm}}^{2}$ were determined, respectively, indicating the Fe acceptor being a recombination center. The capture cross sections were found to be temperature dependent in agreement with a multiphonon emission process with activation energies of 138\ifmmode\pm\else\textpm\fi{}13 meV for electron and 161\ifmmode\pm\else\textpm\fi{}15 meV for hole capture. Measurements of the ${\mathrm{Fe}}^{3+/2+}$ electron capture cross section at electric-field strengths above $4\ifmmode\times\else\texttimes\fi{}{10}^{4}\mathrm{V}/\mathrm{c}\mathrm{m}$ reveal an approximately 70 times higher value of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}{\mathrm{cm}}^{2}$ than without an electric field due to an electric-field-induced lowering of the capture barrier. This increase of the capture cross section is most likely due to a decreased capture barrier for electrons in the $L$ valleys. Since the capture barrier is close to zero when an electric field is applied, the apparent activation energy of ${E}_{C}\ensuremath{-}0.62$ eV, determined by deep-level transient spectroscopy from the carrier emission in an electric field, has not to be corrected by the zero-field capture barrier energy.