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A simple process is developed to curl graphene membranes through thermal annealing. The resulting curled graphene ribbons displayed enhanced photocurrent response compared to flat graphene ribbons. The annealing temperature, the thickness of the graphene, and the type of poly-methyl methacrylate used were the three key factors that influenced the morphology of graphene during thermal annealing. Each of the factors has been systematically investigated, and the transition from flat to curled graphene ribbons was observed. This work has shown a facile method to alter graphene morphology and to develop promising graphene structures for future optoelectronics.