An extensive amount of research has been focused on the development of state-of-the-art methodologies for drug administration. In this study, we have utilized density functional theory (DFT) for assessing the ability of a Twin monolayer of boron nitride and graphene, i.e., Twin-BN and Twin-Gr monolayer, as a carrier for delivering four anticancer drugs (ACDs) 5-fluorouracil (5-FU), gemcitabine (GC), cyclophosphamide (CP), and mercaptopurine (6-MP). Also, the properties of all drug molecules along with the Twin-BN and Twin-Gr and the complex of the ACD-Twin-BN/Gr monolayer were investigated to explore the usefulness of the Twin-BN and Twin-Gr monolayer as ACD carrier. The interaction between the monolayers and ACDs confirmed that the adsorption is feasible as the adsorption energy ranged from -0.41 eV to -0.95 eV in the case of Twin-BN, while it ranged from -0.43 eV to -0.61 eV in the case of Twin-Gr. Additionally, the change in the band gap of the Twin-BN and Twin-Gr monolayers after the adsorption of ACDs was considerable. We can conclude that among both monolayers, Twin-BN can be utilized as a highly effective carrier for delivering ACDs. Our findings showed that the monolayer Twin-BN could be explored as a drug transporter for highly efficient carrying of the considered ACDs.