Rheumatoid arthritis (RA) is a debilitating autoimmune disorder with an inflammatory condition targeting the joints that affects millions of patients worldwide. Several unmet needs still need to be addressed despite recent improvements in the management of RA. Although current RA therapies can diminish inflammation and alleviate symptoms, many patients remain unresponsive or experience flare-ups of their ailment. The present study aims to address these unmet needs through in silico research, with a focus on the identification of novel, potentially active molecules. Therefore, a molecular docking analysis has been conducted using AutoDockTools 1.5.7 on Janus kinase (JAK) inhibitors that are either approved for RA or in advanced phases of research. The binding affinities of these small molecules against JAK1, JAK2, and JAK3, which are target proteins implicated in the pathophysiology of RA, have been assessed. Subsequent to identifying the ligands with the highest affinity for these target proteins, a ligand-based virtual screening was performed utilizing SwissSimilarity, starting with the chemical structures of the previously identified small molecules. ZINC252492504 had the highest binding affinity (−9.0 kcal/mol) for JAK1, followed by ZINC72147089 (−8.6 kcal/mol) for JAK2, and ZINC72135158 (−8.6 kcal/mol) for JAK3. Using SwissADME, an in silico pharmacokinetic evaluation showed that oral administration of the three small molecules may be feasible. Based on the preliminary results of the present study, additional extensive research is required for the most promising candidates to be conducted so their efficacy and safety profiles can be thoroughly characterized, and they can become medium- and long-term pharmacotherapeutic solutions for the treatment of RA.