We present results of imaging polarimetry of the H2 v=1--0 S(1) line towards the outflow lobes of DR21. The polarization vectors are produced by dichroic absorption in a medium of aligned grains and therefore delineate the direction of the magnetic field, projected on to the plane of the sky, aligning those grains. It is argued that the polarization is dominated by grains within the DR21 cloud. The magnetic field strength, estimated from the dispersion of position angles of the polarization vectors, is ∼ 0.07 mG, which is not sufficient to play a significant role in either halting the outflow or confining its lateral expansion.The polarimetry of the H2v=1--0 S(1) line suggests that the magnetic field is parallel to the outflow axis for the eastern outflow lobe, whereas it appears twisted perpendicular to this axis for the western lobe. This peculiar morphology for the magnetic field may imply the presence of either a two-component magnetic field along the line of sight or a complex, wound-up magnetic field.