This phase I trial studies the side effects and best dose of ipilimumab when given after chemoradiation therapy in treating patients with stages IB2-IIB or IIIB-IVA cervical cancer. Drugs used in chemotherapy, such as cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Radiation therapy uses high-energy x-rays to kill tumor cells and shrink tumors. Monoclonal antibodies, such as ipilimumab, may find tumor cells and help carry tumor-killing substances to them. Giving ipilimumab together with chemoradiation therapy may be a better way treat cervical cancer.