In recent years, there has been extensive research on the memristor, a non-volatile memory device that demonstrates effective emulation of biological synapses. The implementation of graphene as a top electrode in memristive switching systems presents an intriguing alternative to conventional materials such as Platinum. Graphene, as a carbon-derived material, possesses a remarkable area- to-volume ratio, biocompatibility, adsorption capabilities, and high electrical conductivity and thereby offers a promising avenue for the fabrication of biosensors with superior characteristics. This study reports a novel fabrication method of utilizing graphene as a top electrode in memristive devices. Characterization results of micrometric devices as well as larger memristive devices are also discussed. Larger devices show promising results to be used as memristive sensors. Microstructures have been fabricated successfully through developing a process flow and patterning graphene using photolithography and lift-off. E-beam evaporation and sputtering were used for depositing bottom metal electrodes and active layer respectively. Graphene was produced using the chemical vapor deposition (CVD) method and subsequently transferred using the fishing technique. Ultimately Pt/TiO2/TiOx/Graphene memristive devices were fabricated.