Finding an inexpensive and scalable method for the mass production of memristors will be one of the key aspects for their implementation in end-user computing applications. Herein, we report pioneering research on the fabrication of laser-lithographed graphene oxide memristors. The devices have been surface-fabricated through a graphene oxide coating on a polyethylene terephthalate substrate followed by a localized laser-assisted photo-thermal partial reduction. When the laser fluence is appropriately tuned during the fabrication process, the devices present a characteristic pinched closed-loop in the current-voltage relation revealing the unique fingerprint of the memristive hysteresis. Combined structural and electrical experiments have been conducted to characterize the raw material and the devices that aim to establish a path for optimization. Electrical measurements have demonstrated a clear distinction between the resistive states, as well as stable memory performance, indicating the potential of laser-fabricated graphene oxide memristors in resistive switching applications.