Inclusion Criteria:

          -  Recurrent or persistent cervical cancer after prior systemic chemotherapy for which
             there is no curative intent option

          -  Documented histologic cervical cancer (acceptable histologies: squamous carcinoma,
             adenocarcinoma, and adenosquamous carcinoma)

          -  Patients must have PD-L1 tumor positivity as defined as CPS>/= 1

          -  Age greater than 18 and ECOG performance status of <= 2

          -  Adequate organ and marrow function

        Exclusion Criteria:

          -  Prior treatment with cabozantinib or pembrolizumab

          -  Receipt of any type of small molecule kinase inhibitor

          -  Receipt of any type of cytotoxic, biologic or other systemic anticancer therapy

          -  Radiation therapy for bone metastasis within 2 weeks, any other radiation therapy
             within 4 weeks before first dose of study treatment

          -  Known brain metastases or cranial epidural disease unless adequately treated with
             radiotherapy and/or surgery

          -  Anticoagulation with oral anticoagulants (eg, warfarin, direct thrombin and Factor Xa
             inhibitors) or platelet inhibitors (eg, clopidogrel)

          -  Uncontrolled, significant intercurrent or recent illness including, but not limited
             to, the following conditions: Cardiovascular disorders: Congestive heart failure New
             York Heart Association Class 3 or 4, unstable angina pectoris, serious cardiac
             arrhythmias Uncontrolled hypertension despite optimal antihypertensive treatment,
             stroke

          -  Gastrointestinal (GI) disorders including those associated with a high risk of
             perforation or fistula formation

          -  Clinically significant hematuria, hematemesis, or hemoptysis of > 0.5 teaspoon (2.5
             ml) of red blood, or other history of significant bleeding (eg, pulmonary hemorrhage)
             within 12 weeks before first dose

          -  Active autoimmune disease requiring systemic therapy within the past 2 years

          -  Active infection requiring systemic therapy within the past month

          -  History of immunodeficiency