Transcranial direct current stimulation (tDCS) modulates cortical excitability and when applied in combination with a cognitive task has potential to enhance performance. In the speech domain, previous work indicated that anodal tDCS over left motor cortex and right cerebellum increased the magnitude of speech adaptation during sensorimotor learning. Here, we aimed to replicate these findings in a pre-registered, double-blind, randomised, sham-controlled study of a large sample (three groups of N = 30). Participants read words out loud. Speech was recorded and fed back to them either normally or with a 110-Mel increase in the frequency of the first vowel formant. Participants responded to altered feedback by changing their speech production (adaptation). Participants were randomly allocated to receive 2-mA anodal tDCS over either left speech motor cortex, or right cerebellum, or sham stimulation. We tested for differences in speech adaptation among the three groups using one-way analyses of variance. We also explored the relationship between speech adaptation and measures of speech perception. All groups showed significant adaptation while receiving altered auditory feedback. Contrary to the previous study, we found no impact of anodal tDCS on the magnitude of the speech adaptation. In conclusion, speech adaptation was unaffected by anodal tDCS over speech motor cortex or cerebellum. This study is another example of the inconsistent effects of tDCS on task performance particularly when participants are young and healthy. Even larger samples may be needed to detect small effects and to avoid spurious results arising from individual differences in task performance.