We report measurement of terahertz anomalous Hall conductivity and Faraday rotation in the magnetic Weyl semimetal ${\mathrm{Co}}_{2}\mathrm{MnGa}$ thin films as a function of the magnetic field, temperature, and thickness, using time-domain terahertz spectroscopy. The terahertz conductivity shows a thickness-independent anomalous Hall conductivity of around 600 ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ at room temperature, and it is also frequency-independent from 0.2--1.5 THz. The magnitude of the longitudinal and Hall conductivities, the weak spin-orbit coupling, and the very close positioning of Weyl points to the chemical potential all satisfy the criteria for intrinsic anomalous Hall conductivity. First-principles calculation also supports the frequency-independent intrinsic anomalous Hall conductivity at low frequency. We also find a thickness-independent Faraday rotation of 59 $(\ifmmode\pm\else\textpm\fi{}6)$ mrad at room temperature, which comes from the intrinsic Berry curvature contribution. In the thinnest 20 nm sample, the Faraday rotation divided by the sample thickness reaches around 3 mrad/nm due to Berry curvature, and is the largest reported at room temperature. The giant Verdet constant of the order of ${10}^{6}$ rad ${\mathrm{m}}^{\ensuremath{-}1} {\mathrm{T}}^{\ensuremath{-}1}$ at room temperature and the large Hall angle around $8.5%$ from 0.2--1.5 THz indicate that ${\mathrm{Co}}_{2}\mathrm{MnGa}$ is promising for THz spintronics at room temperature.