Stroke is a leading cause of adult disability. The ability to live independently after stroke depends on the recovery of motor function. This research will investigate whether transcranial direct current stimulation (tDCS) can increase the rate and extent of motor recovery after stroke. TDCS is a safe, painless and non-invasive way to increase the activity of the stroke side of the brain. Previous studies have shown that applying tDCS during physiotherapy can enhance the benefits of therapy. However, little is known about its effects with patients at the sub-acute stage. This feasibility study will evaluate patient and therapist acceptance of tDCS and estimate effect size and recruitment rate. If feasible, tDCS will be integrated with rehabilitation after stroke in a multi-centre, double-blind, randomised controlled trial. This research has the potential to improve the recovery of motor function and independence for the approximately 6000 New Zealanders who experience stroke each year.