Graphene has become a prominent material in cancer research in recent years. Graphene and its derivatives also attract attention as carriers in drug delivery systems. In this study, we designed a graphene oxide (GO)-based methotrexate (MTX)-loaded and folic acid (FA)-linked drug delivery system. MTX and FA were bound to GO synthesized from graphite. MTX/FA/GO drug delivery system and system components were characterized using Fourier transform infrared spectroscopy (FTIR), differential calorimetric analysis (DSC), scanning electron microscopy (SEM), transmission electron microscopy (TEM), zeta potential analysis, and dimension measurement (DLS) studies. SEM and TEM images confirmed the nanosheet structure of GO synthesized from graphite, and it was shown that MTX/FA binding to GO transformed the two-dimensional GO into a three-dimensional structure. FTIR and DSC graphs confirmed that oxygen atoms were bound to GO with the formation of carboxylic, hydroxyl, epoxide, and carbonyl groups as a result of the oxidation of graphite, and GO was successfully synthesized. Additionally, these analyses showed that MTX and FA bind physicochemically to the structure of GO. The in vitro Franz diffusion test was performed as a release kinetic test. The release kinetics mathematical model and correlation coefficient (R2) of MTX-loaded GO/FA nanomaterials were found to be the Higuchi model and 0.9785, respectively. Stiffness analyses showed that adding FA to this release system facilitated the entry of the drug into the cell by directing the system to target cells. As a result of the stiffness analyses, the stiffness values of the control cell group, free MTX, and MTX/FA/GO applied cells were measured as 2.34 kPa, 1.87 kPa, and 1.56 kPa, respectively. According to these results, it was seen that MTX/FA/GO weakened the cancer cells. Combined use of the MTX/FA/GO drug delivery system had a higher cytotoxic effect than free MTX on the MDA-MB-231 breast cancer cell line. The results showed that the synthesized MTX/FA/GO material has promising potential in cancer cell-specific targeted therapy for MTX as a drug delivery system.