Given the increase in current density in the constituent materials of electrical systems, improving the electrical conductivity of these materials, particularly copper (Cu), is crucial. This would also help to mitigate the heat generated by Joule heating. The incorporation of graphene (Gr) into a composite material (Cu/Gr) is a viable solution. However, to ensure the proper transfer of properties between the reinforcement and the matrix, several elements must be considered, including the orientation of the reinforcement. As a 2D material, controlling graphene’s orientation within the structure is essential but often overlooked. To address this issue, hot rolling was implemented to improve the alignment of the reinforcement. The inclusion of graphene led to a 12 HV increase in the material’s hardness, demonstrating a positive composite effect. Simultaneously, rolling increased the material’s hardness from 67.6 to 75.1 HV by introducing more dislocations into the material. To characterize the graphene’s alignment, polarized Raman spectroscopy was used. This technique highlighted the improved alignment of the reinforcement in the rolling direction, a change that was visible and confirmed by scanning electron microscopy micrographs.