We present HI observations of the elliptical galaxy NGC 2974, obtained with the Very Large Array. These observations reveal that the previously detected HI disc in this galaxy (Kim et al. 1988) is in fact a ring. By studying the harmonic expansion of the velocity field along the ring, we constrain the elongation of the halo and find that the underlying gravitational potential is consistent with an axisymmetric shape. We construct mass models of NGC 2974 by combining the HI rotation curve with the central kinematics of the ionised gas, obtained with the integral-field spectrograph SAURON. We introduce a new way of correcting the observed velocities of the ionised gas for asymmetric drift, and hereby disentangle the random motions of the gas caused by gravitational interaction from those caused by turbulence. To reproduce the observed flat rotation curve of the HI gas, we need to include a dark halo in our mass models. A pseudo-isothermal sphere provides the best model to fit our data, but we also tested an NFW halo and Modified Newtonian Dynamics (MOND), which fit the data marginally worse. The mass-to-light ratio M/L_I increases in NGC 2974 from 4.3 (M/L_I)sun at one effective radius to 8.5 (M/L_I)sun at 5 Re. This increase of M/L already suggests the presence of dark matter: we find that within 5 Re at least 55 per cent of the total mass is dark.