Continuous studies are being carried out to explore new methods and carrier surfaces for target drug delivery. Herein, we report the covalent triazine framework C6N6 as a drug delivery carrier for fluorouracil (FU) and nitrosourea (NU) anti-cancer drugs. FU and NU are physiosorbed on C6N6 with adsorption energies of −28.14 kcal/mol and −27.54 kcal/mol, respectively. The outcomes of the non-covalent index (NCI) and quantum theory of atoms in molecules (QTAIM) analyses reveal that the FU@C6N6 and NU@C6N6 complexes were stabilized through van der Waals interactions. Natural bond order (NBO) and electron density difference (EDD) analyses show an appreciable charge transfer from the drug and carrier. The FU@C6N6 complex had a higher charge transfer (−0.16 e−) compared to the NU@C6N6 complex (−0.02 e−). Frontier molecular orbital (FMO) analysis reveals that the adsorption of FU on C6N6 caused a more pronounced decrease in the HOMO-LUMO gap (EH-L) compared to that of NU. The results of the FMO analysis are consistent with the NBO and EDD analyses. The drug release mechanism was studied through dipole moments and pH effects. The highest decrease in adsorption energy was observed for the FU@C6N6 complex in an acidic medium, which indicates that FU can easily be off-loaded from the carrier (C6N6) to a target site because the cancerous cells have a low pH compared to a normal cell. Thus, it may be concluded that C6N6 possesses the therapeutic potential to act as a nanocarrier for FU to treat cancer. Furthermore, the current study will also provide motivation to the scientific community to explore new surfaces for drug delivery applications.