Transcranial direct current stimulation (tDCS) modulates cortical excitability in a polarity-specific way and, when used in combination with a behavioural task, it can alter performance. TDCS has the potential, therefore, for use as an adjunct to therapies designed to treat disorders affecting speech, including, but not limited to acquired aphasias and developmental stuttering. For this reason, it is important to conduct studies evaluating its effectiveness and the parameters optimal for stimulation. Here, we aimed to evaluate the effects of bi-hemispheric tDCS over speech motor cortex on performance of a complex speech motor learning task, namely the repetition of tongue twisters. A previous study in older participants showed that tDCS could modulate performance on a similar task. To further understand the effects of tDCS, we also measured the excitability of the speech motor cortex before and after stimulation. Three groups of 20 healthy young controls received: (i) anodal tDCS to the left IFG/LipM1 and cathodal tDCS to the right hemisphere homologue; or (ii) cathodal tDCS over the left and anodal over the right; or (iii) sham stimulation. Participants heard and repeated novel tongue twisters and matched simple sentences before, during and 10 min after the stimulation. One mA tDCS was delivered concurrent with task performance for 13 min. Motor excitability was measured using transcranial magnetic stimulation to elicit motor-evoked potentials in the lip before and immediately after tDCS. The study was double-blind, randomized, and sham-controlled; the design and analysis were pre-registered. Performance on the task improved from baseline to after stimulation but was not significantly modulated by tDCS. Similarly, a small decrease in motor excitability was seen in all three stimulation groups but did not differ among them and was unrelated to task performance. Bayesian analyses provide substantial evidence in support of the null hypotheses in both cases, namely that tongue twister performance and motor excitability were not affected by tDCS. We discuss our findings in the context of the previous positive results for a similar task. We conclude that tDCS may be most effective when brain function is sub-optimal due to age-related declines or pathology. Further study is required to determine why tDCS failed to modulate excitability in the speech motor cortex in the expected ways.