We investigate the evolution of the relative angle between the stellar rotation axis and the circumstellar disc axis of a star that forms in a stellar cluster from the collapse of a turbulent molecular cloud. This is an inherently chaotic environment with variable accretion, both in terms of rate and the angular momentum of the material, and dynamical interactions between stars. We find that the final stellar rotation axis and disc spin axis can be strongly misaligned, but this occurs primarily when the disc is truncated by a dynamical encounter so that the final disc rotation axis depends simply on what fell in last. This may lead to planetary systems with orbits that are misaligned with the stellar rotation axis, but only if the final disc contains enough mass to form planets. We also investigate the time variability of the inner-disc spin axis, which is likely to determine the direction of a protostellar jet. We find that the jet direction varies more strongly for lighter discs, such as those that have been truncated by dynamical interactions or have suffered a period of rapid accretion. Finally, we note that variability of the angular momentum of the material accreted by a star implies that the internal velocity field of such stars may be more complicated than that of aligned differential rotation.