Résumé
We report the detection of a large-scale magnetic field at the surface of the slowly-rotating fully-convective M dwarf Proxima Centauri. Ten circular polarization spectra, collected from April to July 2017 with the HARPS-Pol spectropolarimeter, exhibit rotationally-modulated Zeeman signatures suggesting a stellar rotation period of $89.8 \pm 4.0$ d. Using Zeeman-Doppler Imaging, we invert the circular polarization spectra into a surface distribution of the large-scale magnetic field. We find that Proxima Cen hosts a large-scale magnetic field of typical strength 200 G, whose topology is mainly poloidal, and moderately axisymmetric, featuring, in particular, a dipole component of 135 G tilted at 51$^{\circ}$ to the rotation axis. The large-scale magnetic flux is roughly 3 times smaller than the flux measured from the Zeeman broadening of unpolarized lines, which suggests that the underlying dynamo is efficient at generating a magnetic field at the largest spatial scales. Our observations occur $\sim$1 yr after the maximum of the reported 7 yr-activity cycle of Proxima Cen, which opens the door for the first long-term study of how the large-scale field evolves with the magnetic cycle in a fully-convective very-low-mass star. Finally, we find that Proxima Cen's habitable zone planet, Proxima-b, is likely orbiting outside the Alfv\`en surface, where no direct magnetic star-planet interactions occur.