Perceptual-motor synchronisation in human groups is crucial in many activities, from musical ensembles to sports teams. To this aim, the mirror game, where partners are asked to imitate each other's movements or gestures, is one of the best available experimental paradigms to study how humans engage in joint tasks and how they tend to synchronise their behaviour. However, to date, virtual reality characters do not engage in motor synchronisation with human users. In this work, we explored to what extent an autonomous virtual character and a human that play the mirror game in virtual reality can synchronise their behaviour. We created a full-body version of the mirror game with an autonomous virtual character, whose movements were driven by a model based on coupled oscillators. Participants engaged in a joint imitation task with a virtual player animated with one of three options: a model that included a small coupling, a model with no coupling, or another human. Behavioural measures and subjective reports suggest that participants were unable to distinguish the condition of small coupling from the engagement with an avatar driven by another human participant.