A Study Comparing Upadacitinib (ABT-494) to Placebo in Participants With Active Psoriatic Arthritis Who Have a History of Inadequate Response to at Least One Biologic Disease Modifying Anti-Rheumatic Drug

* Clinical diagnosis of PsA with symptom onset at least 6 months prior to the Screening Visit and fulfillment of the Classification Criteria for PsA (CASPAR) criteria * Participant has active disease at Baseline defined as \>= 3 tender joints (based on 68 joint counts) and \>= 3 swollen joints (based on 66 joint counts) at Screening and Baseline Visits * Diagnosis of active plaque psoriasis or documented history of plaque psoriasis * Participant has had an inadequate response (lack of efficacy after a minimum 12 week duration of therapy) or intolerance to treatment with at least 1 bDMARD.

* Prior exposure to any Janus Kinase (JAK) inhibitor (including but not limited to ruxolitinib, tofacitinib, baricitinib, and filgotinib) * Current treatment with \> 2 non-biologic DMARDs or use of DMARDs other than Methotrexate (MTX), Sulfasalazine (SSZ), Leflunomide (LEF), apremilast, Hydroxychloroquine (HCQ), bucillamine or iguratimod or use of MTX in combination with LEF at Baseline. * History of fibromyalgia, any arthritis with onset prior to age 17 years, or current diagnosis of inflammatory joint disease other than PsA (including, but not limited to rheumatoid arthritis, gout, overlap connective tissue diseases, scleroderma, polymyositis, dermatomyositis, systemic lupus erythematosus). Prior history of reactive arthritis or axial spondyloarthritis including ankylosing spondylitis and non-radiographic axial spondyloarthritis is permitted if documentation of change in diagnosis to PsA or additional diagnosis of PsA is made. Prior history of fibromyalgia is permitted if documentation of change in diagnosis to PsA or documentation that the diagnosis of fibromyalgia was made incorrectly.