The merger remnant NGC 1316 (Fornax A) is one of the most important objects regarding the investigation of and thus an important object to study merger-related processes. A recent photometric study used globular clusters in NGC 1316 to constrain its star formation history, but without the knowledge of individual radial velocities. The kinematical properties of the globular cluster system in comparison with the diffuse stellar light might give more insight into the formation of NGC 1316. Of particular interest is the dark matter content. Planetary nebulae in NGC 1316 indicate a massive dark halo, and globular cluster velocities provide independent evidence. We aim at measuring radial velocities of globular clusters in NGC 1316. We use these kinematical data to investigate the global structure of NGC 1316 and to constrain the dark matter content. We perform multiobject spectroscopy with VLT/FORS2 and MXU. Out of 562 slits, we extract radial velocities for 177 globular clusters. Moreover, we measure radial velocities of the integrated galaxy light, using slits with a sufficiently bright sky. To these data, we add 20 cluster velocities from the literature. In an appendix, we identify new morphological features of NGC 1316 and its companion galaxy NGC 1317.