Evidence suggests that temporal predictions arising from the motor system can enhance auditory perception. However, in speech perception, we lack evidence of perception being modulated by production. Here we show a behavioural protocol that captures the existence of such auditory-motor interactions. Participants performed a syllable discrimination task immediately after producing periodic syllable sequences. Two speech rates were explored: a 'natural' (individually preferred) and a fixed 'non-natural' (2 Hz) rate. Using a decoding approach, we show that perceptual performance is modulated by the stimulus phase determined by a participant's own motor rhythm. Remarkably, for 'natural' and 'non-natural' rates, this finding is restricted to a subgroup of the population with quantifiable auditory-motor coupling. The observed pattern is compatible with a neural model assuming a bidirectional interaction of auditory and speech motor cortices. Crucially, the model matches the experimental results only if it incorporates individual differences in the strength of the auditory-motor connection.