From observations with the GMOS multislit spectrograph on the Gemini North telescope, we have obtained spectra for 39 globular cluster (GC) candidates in the Virgo giant elliptical galaxy NGC 4649 (M60), of which 38 are confirmed GCs. The clusters extend out to a radius of 260 arcsec (3.5 effective radii). We find no rotation of the GC system, with an upper limit of v/σ < 0.6 at a confidence level of 95 per cent. The GC velocity dispersion is constant with radius, within the uncertainties. We fit isotropic models to the GC and stellar kinematics; these models yield an (M/L)V around 16 at 200 arcsec radius (16 kpc), an increase of a factor of 2 from the central M/L. We also use the mass profile as derived from X-rays to determine the orbital structure. Using axisymmetric orbit-based models and the X-ray mass profile, we find the orbital distribution is close to isotropic within 100 arcsec, and becomes tangentially biased beyond. Furthermore, when using the X-ray profile, we find a better fit to the kinematics compared to using a constant M/L model. Thus, both isotropic and axisymmetric orbit-based models give support for the presence of a dark matter halo in NGC 4649.