To stop the COVID-19 pandemic due to the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), which caused more than 2.5 million deaths to date, new antiviral molecules are urgently needed. The replication of SARS-CoV-2 requires the RNA-dependent RNA polymerase (RdRp), making RdRp an excellent target for antiviral agents. RdRp is a multi-subunit complex composed of 3 viral proteins named nsp7, nsp8 and nsp12 that ensure the ~30 kb RNA genome's transcription and replication. The main strategies employed so far for the overproduction of RdRp consist of expressing and purifying the three subunits separately before assembling the complex in vitro. However, nsp12 shows limited solubility in bacterial expression systems and is often produced in insect cells. Here, we describe an alternative strategy to co-express the full SARS-CoV-2 RdRp in E. coli, using a single plasmid. Characterization of the purified recombinant SARS-CoV-2 RdRp shows that it forms a complex with the expected (nsp7)(nsp8)2(nsp12) stoichiometry. RNA polymerization activity was measured using primer-extension assays showing that the purified enzyme is functional. The purification protocol can be achieved in one single day, surpassing in speed all other published protocols. Our construct is ideally suited for screening RdRp and its variants against very large chemical compounds libraries and has been made available to the scientific community through the Addgene plasmid depository (Addgene ID: 165451).