Clusters of galaxies are the largest gravitationally bound objects in the Universe, containing about 10sup 15 solar masses of hot (10sup 8 K) gas, galaxies and dark matter in a typical volume of 10 Mpcsup 3. Magnetic fields and relativistic particles are mixed with the gas as revealed by giant 'radio haloes', which arise from diffuse, megaparsec-scale synchrotron radiation at cluster centre. Radio haloes require that the emitting electrons are accelerated in situ (by turbulence), or are injected (as secondary particles) by proton collisions into the intergalactic medium. They are found only in a fraction of massive clusters that have complex dynamics, which suggests a connection between these mechanisms and cluster mergers. Here we report a radio halo at low frequencies associated with the merging cluster Abell 521. This halo has an extremely steep radio spectrum, which implies a high frequency cut-off; this makes the halo difficult to detect with observations at 1.4 GHz (the frequency at which all other known radio haloes have been best studied). The spectrum of the halo is inconsistent with a secondary origin of the relativistic electrons, but instead supports turbulent acceleration, which suggests that many radio haloes in the Universe should emit mainly at low frequencies. PUBLICATION ABSTRACT