This paper presents further results from our spectroscopic study of the globular cluster (GC) system of the group elliptical NGC 3923. From observations made with the GMOS instrument on the Gemini South Telescope, an additional 50 GC and ultra-compact dwarf (UCD) candidates have been spectroscopically confirmed as members of the NGC 3923 system. When the recessional velocities of these GCs are combined with the 29 GC velocities reported previously, a total sample of 79 GC/UCD velocities is produced. This sample extends to over 6 arcmin (> 6 Re∼ 30 kpc) from the centre of NGC 3923 and is used to study the dynamics of the GC system and the dark matter content of NGC 3923. It is found that the GC system of NGC 3923 displays no appreciable rotation, and that the projected velocity dispersion is constant with radius within the uncertainties. The velocity dispersion profiles of the integrated light and GC system of NGC 3923 are indistinguishable over the region in which they overlap. We find some evidence that the diffuse light and GCs of NGC 3923 have radially biased orbits within ∼130 arcsec. The application of axisymmetric orbit-based models to the GC and integrated light velocity dispersion profiles demonstrates that a significant increase in the mass-to-light ratio (from M/LV= 8 to 26) at large galactocentric radii is required to explain this observation. We therefore confirm the presence of a dark matter halo in NGC 3923. We find that dark matter comprises 17.5 per cent of the mass within 1 Re, 41.2 per cent within 2 Re and 75.6 per cent within the radius of our last kinematic tracer at 6.9 Re. The total dynamical mass within this radius is found to be M⊙. In common with other studies of large ellipticals, we find that our derived dynamical mass profile is consistently higher than that derived by X-ray observations, by a factor of around 2.