The recent outbreak of the SARS-CoV-2 infection has affected the lives and economy of more than 200 countries. The unavailability of vaccines and the virus-specific drugs has created an opportunity to repurpose existing drugs to examine their efficacy in controlling the virus activities. Here, the inhibition of the RdRp viral protein responsible for the replication of the virus in host cells is examined by evaluating the binding patterns of various approved and investigational antiviral, antibacterial, and anti-cancer drugs by using the molecular docking approach. Some of these drugs have been proposed to be effective against the SARS-Cov-2 virus infection. In an attempt to discover new antiviral agents, artificially expanded genetic alphabets (AEGIS) such as dP, dZ, dJ, dV, dX, dK, dB, dS, dP4, and dZ5 and different sequences of these nucleotides were also docked into the active site of the RdRp protein. It is found that among the various approved and investigational drugs, the Clevudine, N4-hydroxycytidine (EIDD-1931), 2'-C-methylcytidine, EIDD-2801, Uprifosbuvir, Balapiravir, Acalabrutinib, BMS-986094, Remdesivir (full drug), GS-6620, and Ceforanide would act as potent inhibitors of the RdRp protein. Similarly, among the AEGIS nucleotides, dB, dJ, dP, dK, dS, dV, and dZ are found to inhibit the RdRp protein efficiently. It is further found that sequences containing up to three artificial nucleotides can also inhibit the RdRp viral protein. As these unnatural nucleotides are foreign molecules for the cells, their replication in host cells may not occur naturally, and hence these may act as potent drugs for the treatment of the SARS-CoV-2 infection. However, in vivo evaluation of these drugs and artificial nucleotides are required against SARS-CoV-2 before prescribing them to the infected patients.