Applying a weak electrical current to the cortex can have effects on a range of behaviours. Techniques such as transcranial direct current stimulation (tDCS) have been widely used in both research and clinical settings. However, there is significant variability across individuals in terms of their responsiveness to stimulation, which poses practical challenges to the application of tDCS, but also provides a unique opportunity to study the link between the brain and behaviour. Here, we assessed the role of individual differences in cortical morphology - specifically in prefrontal cortical regions of interest - for determining the influence of tDCS on decision-making performance. Specifically, we employed magnetic resonance imaging (MRI) and a previously replicated paradigm in which we modulated learning in a simple decision-making task by applying tDCS to the left prefrontal cortex in human subjects of both sexes. Cortical thickness of the left (but not right) prefrontal cortex accounted for almost 35% of the variance in stimulation efficacy across subjects. This is the first demonstration that variations in cortical architecture are associated with reliable differences in the effects of tDCS on cognition. Our findings have important implications for predicting the likely efficacy of different non-invasive brain stimulation treatments on a case by case basis.