We present the outcome of a highly-sensitive search for magnetic fields on the cool supergiant Betelgeuse. A time-series of six circularly polarized spectra was obtained using the NARVAL spectropolarimeter at Télescope Bernard Lyot (Pic du Midi Observatory (F)), between March and April 2010. Zeeman signatures were repeatedly detected in cross-correlation profiles, corresponding to a longitudinal component of about 1 G. The time-series unveils a smooth increase of the longitudinal field from 0.5 to 1.5 G, correlated with radial velocity fluctuations. We observe a strong asymmetry of Stokes V signatures, also varying in correlation with the radial velocity. The Stokes V line profiles are red-shifted by about 9 km s^-1 with respect to the Stokes I profiles, suggesting that the observed magnetic elements may be concentrated in the sinking components of the convective flows.