Inclusion Criteria:  Subjects must have recurrent low-grade serous ovarian cancer. Up to 5 prior lines of therapy are allowed. Prior therapy with MEK inhibitors is allowed Prior therapy with aromatase inhibitors like letrozole is allowed Prior anti-angiogenesis therapy is not allowed except for bevacizumab. Subjects must have measurable disease based on RECIST 1.1 with at least one target lesion and with available archival tumor tissue. Subjects must have an ECOG performance status of 0-2. Age ≥ 18 years. Life expectancy of at least 12 weeks (3 months). Subjects must be able to understand and be willing to sign the written informed consent form. A signed informed consent form must be appropriately obtained prior to the conduct of any trial-specific procedure.  Adequate bone marrow, liver and renal function as assessed by the following laboratory requirements:  Total bilirubin ≤ 1.5 x the upper limits of normal (ULN) Alanine aminotransferase (ALT) and aspartate amino-transferease (AST) ≤ 2.5 x ULN (≤ 5 x ULN for subjects with liver involvement of their cancer) Alkaline phosphastase limit ≤ 2.5 x ULN (≤ 5 x ULN for subjects with liver involvement of their cancer) Serum creatinine ≤ 1.5 x the ULN International normalized ratio (INR)/ Partial thromboplastin time (PTT) ≤ 1.5 x ULN. (Subjects who are treated with an agent such as warfarin or heparin will be allowed to participate provided that no prior evidence of underlying abnormality in coagulation parameters exists. Close monitoring of at least weekly evaluations will be performed until INR/PTT is stable based on a measurement that is pre-dose as defined by the local standard of care. Platelet count >100000 /mm3, hemoglobin (Hb) >9 g/dL, absolute neutrophil count (ANC)> 1500/mm3. Blood transfusion to meet the inclusion criteria will not be allowed. Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of study drug. Post-menopausal women (defined as no menses for at least 1 year) and surgically sterilized women are not required to undergo a pregnancy test. The definition of adequate contraception will be based on the judgment of the investigator. Subjects (women) of childbearing potential must agree to use adequate contraception beginning at the signing of the ICF until at least 2 months after the last dose of study drug. The definition of adequate contraception will be based on the judgment of the principal investigator or a designated associate. Subject must be able to swallow and retain oral medication.  Exclusion Criteria:  Patients with sarcoma, carcinosarcoma or high grade carcinoma Any histology type other than low-grade serous histology Previous assignment to treatment during this study. Subjects permanently withdrawn from study participation will not be allowed to re-enter study. Uncontrolled hypertension (systolic pressure >140 mm Hg or diastolic pressure > 90 mm Hg [NCI-CTCAE v5.0] on repeated measurement) despite optimal medical management.  Active or clinically significant cardiac disease including:  Congestive heart failure - New York Heart Association (NYHA) > Class II. Active coronary artery disease. Cardiac arrhythmias requiring anti-arrhythmic therapy other than beta blockers or digoxin. Unstable angina (anginal symptoms at rest), new-onset angina within 3 months before randomization, or myocardial infarction within 6 months before randomization. Evidence or history of bleeding diathesis or coagulopathy. Any hemorrhage or bleeding event ≥ NCI CTCAE Grade 3 within 4 weeks prior to start of study medication. Subjects with thrombotic, embolic, venous, or arterial events, such as cerebrovascular accident (including transient ischemic attacks) deep vein thrombosis or pulmonary embolism within 6 months of start of study treatment within 6 months of informed consent. Patients with any previously untreated or concurrent cancer that is distinct in primary site or histology except cervical cancer in-situ, treated ductal carcinoma in situ of the breast, curatively treated nonmelanoma skin carcinoma, noninvasive aerodigestive neoplasms, or superficial bladder tumor. Subjects surviving a cancer that was curatively treated and without evidence of disease for more than 3 years before registration are allowed. All cancer treatments must be completed at least 3 years prior to registration. Patients with phaeochromocytoma. Known history of human immunodeficiency virus (HIV) infection or current chronic or active hepatitis B or C infection requiring treatment with antiviral therapy. However, patients with chronic HIV with undetectable viral load by PCR, without opportunistic infection, and on a stable regimen of antiretroviral therapy and patients with chronic hepatitis B or C infection with undetectable viral load by PCR and on a stable regimen of antiretroviral therapy would be eligible. Ongoing infection >= Grade 2 NCI-CTCAE v5.0. Symptomatic metastatic brain or meningeal tumors. Presence of a non-healing wound, non-healing ulcer, or bone fracture. Major surgical procedure or significant traumatic injury within 28 days before start of study medication Renal failure requiring hemo-or peritoneal dialysis. Dehydration Grade >1 NCI-CTCAE v5.0. Patients with seizure disorder requiring medication. Persistent proteinuria >= Grade 3 NCI-CTCAE v5.0 (> 3.5 g/24 hrs, measured by urine protein: creatinine ratio on a random urine sample). Interstitial lung disease with ongoing signs and symptoms at the time of informed consent. Pleural effusion or ascites that causes respiratory compromise (≥ NCI-CTCAE version 5.0 Grade 2 dyspnea). History of organ allograft (including corneal transplant). Known or suspected allergy or hypersensitivity to any of the study drugs, study drug classes, or excipients of the formulations given during the course of this trial.  Any malabsorption condition.  1. Gastrointestinal abnormalities including:  Inability to take oral medication; Requirement for intravenous alimentation; Treatment for active peptic ulcer disease in the past 6 months; Active gastrointestinal bleeding, unrelated to cancer, as evidenced by clinically significant hematemesis, hematochezia or melena in the past 3 months without evidence of resolution documented by endoscopy or colonoscopy; Active bowel obstruction (with or without gastrostomy tube) or inability to take oral medications Patients with an active or at risk for bowel perforation or fistula Availability of an archival FFPE tumor tissue block from primary diagnosis specimen, metastatic, or recurrent site. If an FFPE tissue block cannot be provided then 15 unstained slides (10 minimum) will be acceptable. Please refer to the laboratory manual for complete details. Women who are pregnant or breastfeeding. Any condition which, in the investigator's opinion, makes the subject unsuitable for trial participation. Substance abuse, medical, psychological or social conditions that may interfere with the subject's participation in the study or evaluation of the study results. Concurrent anti-cancer therapy (chemotherapy, radiation therapy, surgery, immunotherapy, biologic therapy, or tumor embolization) other than study treatment (regorafenib combined with fulvestrant). Prior use of regorafenib or other agents with similar multi-targeted kinase activity. Concurrent use of another investigational drug or device therapy (i.e., outside of study treatment) during, or within 4 weeks of trial entry (signing of the informed consent form). Major surgical procedure, open biopsy, or significant traumatic injury within 28 days before start of study medication.  Therapeutic anticoagulation with Vitamin-K antagonists (e.g., warfarin) or with heparins and heparinoids are permitted but should be monitored carefully and closely.  o However, prophylactic anticoagulation as described below is allowed:  Infrequent bleeding or elevations in PT-INR have been reported in some subjects taking warfarin while on regorafenib therapy. Therefore, subjects taking concomitant warfarin should be monitored regularly for changes in PT, PT-INR or clinical bleeding episodes. Low dose aspirin (<= 100 mg daily). Prophylactic doses of heparin. Use of any herbal remedy (e.g. St. John's wort [Hypericum perforatum])