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, ESPRESSO, and CARMENES radial velocities, along with new and archival TESS, CHEOPS, and MuSCAT2/3 photometry data. From fitting the available data, we find that the planet has a radius of Rp=0.93+/-0.06R_Earth_ and a mass of Mp=0.95^+0.29^_-0.30_M_Earth_ (a 3.2-sigma measurement of the semi-amplitude K=0.67+/-0.21m/s), and is on an orbit with a period of 12.761418^+0.000060^_-0.000055_d. A variety of techniques were utilised to attenuate stellar activity signals. Gliese 12 b has an equilibrium temperature of Teq=317+/-8K, assuming an albedo of zero, and a density consistent with that of Earth and Venus {rho}=6.4+/-2.4g/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-Teq parameter space, making it a prime target for follow-up observations, including Lyman-alpha studies.