Rheumatoid Arthritis (RA) is a persistent autoimmune disease affecting approximately 0.5-1 percent of the world population. RA prevalence is higher in woman aged between 35 and 50 years than in age matched men, though this difference is less evident among elderly patients. The profound immune specific effects of disrupted JAK 3 (Janus kinase 3) signaling highlight the possibility of therapeutic targeting of JAK3 as a highly specific mode of immune system suppression. To address the above problem which is unendurable to patients and in the hope to cater some respite to such suffering we have targeted JAK 3 protein and JAK/STAT signaling pathway with compounds downloaded from FDA database, and performed screening of all available compounds docked against JAK3 protein. The difference between the target protein and other proteins of the same family was studied using cross docking and the compounds having higher binding affinity to JAK3 protein also showed more selectivity towards the particular protein. Density functional theory and molecular dynamics simulation study was done to study the compounds at their atomic level to know more about their drug likeliness. At the end of the study and based on our analysis we have come up with three FDA approved drugs that can be proposed as a treatment option for Rheumatoid Arthritis.