Small temperate planets are prime targets for exoplanet studies due to their possible similarities with the rocky planets in the Solar system. M dwarfs are promising hosts since the planetary signals are within our current detection capabilities. Gliese 12 b is a Venus-sized temperate planet orbiting a quiet M dwarf. We present here the first precise mass measurement of this small exoplanet. We performed a detailed analysis using HARPS-N (High Accuracy Radial velocity Planet Searcher for the Northern Hemisphere), ESPRESSO (Echelle Spectrograph for Rocky Exoplanets and Stable Spectroscopic Observations), and CARMENES (Calar Alto high-Resolution search for M dwarfs with Exoearths with Near-infrared and optical Echelle Spectrographs) radial velocities, along with new and archival TESS (Transiting Exoplanet Survey Satellite), CHEOPS (CHaracterising ExOPlanet Satellite), and MuSCAT2/3 (Multicolor Simultaneous Camera for studying Atmospheres of Transiting exoplanets) photometry data. From fitting the available data, we find that the planet has a radius of $R_\mathrm{p} = 0.93\pm 0.06 \, \mathrm{R_{\rm{\oplus }}}$ and a mass of $M_\mathrm{p} = 0.95^{+0.29}_{-0.30} \, \mathrm{M_{\rm{\oplus }}}$ (a $3.2\sigma$ measurement of the semi-amplitude $K=0.67\pm 0.21\, \mathrm{m\, s^{-1}}$), and is on an orbit with a period of $12.761418^{+0.000060}_{-0.000055}\, \mathrm{d}$. A variety of techniques were utilized to attenuate stellar activity signals. Gliese 12 b has an equilibrium temperature of $T_\mathrm{eq}=317 \pm 8\, \mathrm{K}$, assuming an albedo of zero, and a density consistent with that of Earth and Venus ($\rho _\mathrm{p}=6.4\pm 2.4\, \mathrm{g\, cm^{-3}}$). We find that Gliese 12 b has a predominantly rocky interior and simulations indicate that it is unlikely to have retained any of its primordial gaseous envelope. The bulk properties of Gliese 12 b place it in an extremely sparsely populated region of both mass─radius and density─$T_\mathrm{eq}$ parameter space, making it a prime target for follow-up observations, including Lyman-$\alpha$ studies.