A Study to Evaluate the Safety and Efficacy of Upadacitinib in Participants With Giant Cell Arteritis

* Diagnosis of giant cell arteritis (GCA) according to the following criteria: * History of erythrocyte sedimentation rate (ESR) \>= 50 mm/hour or high sensitivity C-reactive protein (hsCRP)/CRP \>=1.0 mg/dL * Presence of at least one of the following: Unequivocal cranial symptoms of GCA or Unequivocal symptoms of polymyalgia rheumatica (PMR) * Presence of at least one of the following: temporal artery biopsy revealing features of GCA or evidence of large vessel vasculitis by angiography or cross-sectional imaging such as ultrasound, magnetic resonance imaging (MRI), computed tomography (CT) or positron emission tomography (PET). * Active GCA, either new onset or relapsing, within 8 weeks of Baseline. * Participants must have received treatment with \>=40 mg prednisone (or equivalent) at any time prior to Baseline and be receiving prednisone (or equivalent) \>= 20 mg once daily (QD) at Baseline. * Participants must have GCA that, in the opinion of the investigator, is clinically stable to allow the participant to safely initiate the protocol-defined corticosteroid (CS) taper regimen. * Females must either be postmenopausal or permanently surgically sterile or, practicing at least 1 specified method of birth control through the study.

* Prior exposure to any Janus Kinase (JAK) inhibitor. * Treatment with an interleukin-6 (IL-6) inhibitor within 4 weeks of study start, or prior treatment with an IL-6 inhibitor and experienced a disease flare during treatment. * Use of any of the following systemic immunosuppressant treatments within the specified timeframe prior to study start: * Anakinra within 1 week of study start. * Methotrexate, hydroxychloroquine, cyclosporine, azathioprine, or mycophenolate within 4 weeks of study start. * Oral corticosteroid (CS) for conditions other than GCA within 4 week of study start, or intravenous CS within 4 weeks of study start. * Greater than or equal to 8 weeks for leflunomide if no elimination procedure was followed, or adhere to an elimination procedure. * Cell-depleting agents or alkylating agents including cyclophosphamide within 6 months of study start. * Current or past history of infection including herpes zoster or herpes simplex, human immunodeficiency virus (HIV), active Tuberculosis, active or chronic recurring infection, active hepatitis B or C. * Female who is pregnant, breastfeeding, or considering pregnancy during the study.