The primary purpose of this pilot study is to evaluate the efficacy and safety of Abatacept in subjects with Sjogren's Syndrome (SS). This clinical trial study will enroll and treat 15 subjects with active moderate and severe inflammatory arthritis associated with primary Sjogren's syndrome (pSS) and secondary Sjogren's sybdrine (sSS) with Rheumatoid Arthrits (RA). All subjects will receive Abatacept weekly by Subcutaneous (SC) dosing. Subjects will receive Abatacept by SC injection of 125 mg on day 1 and followed by 125 mg SC weekly thereafter.