Since its emergence in March 2020, the SARS-CoV-2 global pandemic has produced more than 65 million cases and one point five million deaths worldwide. Despite the enormous efforts carried out by the scientific community, no effective treatments have been developed to date. We created a novel computational pipeline aimed to speed up the process of repurposable candidate drug identification. Compared with current drug repurposing methodologies, our strategy is centered on filtering the best candidate among all selected targets focused on the introduction of a mathematical formalism motivated by recent advances in the fields of algebraic topology and topological data analysis (TDA). This formalism allows us to compare three-dimensional protein structures. Its use in conjunction with two in silico validation strategies (molecular docking and transcriptomic analyses) allowed us to identify a set of potential drug repurposing candidates targeting three viral proteins (3CL viral protease, NSP15 endoribonuclease, and NSP12 RNA-dependent RNA polymerase), which included rutin, dexamethasone, and vemurafenib among others. To our knowledge, it is the first time that a TDA based strategy has been used to compare a massive amount of protein structures with the final objective of performing drug repurposing