We present the results of a spectroscopic survey of red giants in the globular cluster Terzan 8 with the aim of studying its kinematics. We derived accurate radial velocities for 82 stars located in the innermost 7 arcmin from the cluster centre identifying 48 bona fide cluster members. The kinematics of the cluster have been compared with a set of dynamical models accounting for the effect of mass segregation and a variable fraction of binaries. The derived velocity dispersion appears to be larger than that predicted for mass-segregated stellar systems without binaries, indicating that either the cluster is dynamically young or it contains a large fraction of binaries (>30 per cent). We detected seven stars with a radial velocity compatible with the cluster systemic velocity but with chemical patterns which stray from those of both the cluster and the Galactic field. These stars are likely members of the Sagittarius stream surrounding this stellar system.