We use new high-resolution H I data from the Australian Square Kilometre Array Pathfinder to investigate the dynamics of the Small Magellanic Cloud (SMC). We model the H I gas component as a rotating disc of non-negligible angular size, moving into the plane of the sky, and undergoing nutation/precession motions. We derive a high-resolution (∼10 pc) rotation curve of the SMC out to R ∼ 4 kpc. After correcting for asymmetric drift, the circular velocity slowly rises to a maximum value of Vc ≃ 55 km s−1 at R ≃ 2.8 kpc and possibly flattens outwards. In spite of the SMC undergoing strong gravitational interactions with its neighbours, its H I rotation curve is akin to that of many isolated gas-rich dwarf galaxies. We decompose the rotation curve and explore different dynamical models to deal with the unknown 3D shape of the mass components (gas, stars, and dark matter). We find that, for reasonable mass-to-light ratios, a dominant dark matter halo with mass MDM(R < 4 kpc) ≃ 1-1.5 × 109 M☉ is always required to successfully reproduce the observed rotation curve, implying a large baryon fraction of 30 per cent-40 per cent. We discuss the impact of our assumptions and the limitations of deriving the SMC kinematics and dynamics from H I observations.