Rucaparib in Nonmetastatic prOstAte With BRCAness

Inclusion Criteria: * Hormone-sensitive, histologically proven adenocarcinoma of the prostate with BRCAness (defined as an alteration in one or more of the following genes: BARD1, BRCA1, BRCA2, BRIP1, CHEK1, CHEK2, FANCA, NBN, PALB2, RAD51C, RAD51D, RAD51, RAD51B) from soft-tissue based genomic testing or liquid biopsy based genomic or genetic testing. Pathogenic or likely pathogenic alterations are accepted. * Eastern Cooperative Oncology Group (ECOG)/Zubrod score of 0-2. * At a minimum, subjects must have received definitive local therapy with curative intent (i.e., prostatectomy, and/or radiation therapy) with or without systemic therapy. * Testosterone level is \> 50 ng/dL. * Be at least 18 years old at the time the informed consent form is signed. * Demonstrate adequate organ function as defined in the table in the protocol, all screening labs should be performed within 28 days of treatment initiation. * Highly effective barrier methods must be used with all sexual activity and contraception methods must be practiced for all subjects throughout the study and for at least 6 months after last rucaparib treatment administration if the risk of conception exists (section 7.2). * Recovery to baseline or Grade ≤ 1 CTCAE v5.0 from toxicities related to any prior treatments within the context of their definitive local therapy for their prostate cancer, unless Adverse Event(s) (AE)(s) are clinically nonsignificant and/or stable on supportive therapy. * Subject is able to provide informed consent and willing to sign an approved consent form that conforms to federal and institutional guidelines. * Subject must have confirmed PSA progression based on at least two time points taken at least one week apart to confirm rising trend. Exclusion Criteria: * Subjects with metastases defined by conventional scans (CT, MRI, Nuclear Medicine (NM) Bone Scan). Disease identified on molecular imaging (e.g. fluciclovine-PET) is not exclusionary. * Arterial or venous thrombi (including cerebrovascular accident), myocardial infarction, admission for unstable angina, cardiac angioplasty, or stenting within the last 90 days prior to screening. * Pre-existing duodenal stent, recent (within \< 3 months) or existing bowel obstruction, and/or any gastrointestinal disorder or defect that would, in the opinion of the Investigator, interfere with absorption of rucaparib. * Inability to swallow tablets. * Evidence or history of clinically significant bleeding disorder per the determination of the treating investigator. * Prior systemic therapy within the past 30 days prior to Day 1 (or 5 half-lives of the drug, whichever is shorter). * Diagnosis of another malignancy within 2 years before first dose of study treatment only if the cancer will either interfere with participant safety or interfere with the primary endpoint, per the judgement of the Principal Investigator. Participants, who have been diagnosed with, superficial skin cancers, or localized, low grade tumors deemed cured or with a prolonged natural history (e.g estimated overall survival \> 5 years) may be included. * Prior treatment with any poly adenosine diphosphate-ribose polymerase (PARP) inhibitor, mitoxantrone, cyclophosphamide, or any platinum based chemotherapy. * Clinically significant (i.e., active) cardiovascular disease at the time of enrollment: congestive heart failure (\> New York Heart Association Classification Class II), or serious cardiac arrhythmia requiring medication. * Other severe acute or chronic medical conditions including cardiovascular, endocrine, neurologic, pulmonary or psychiatric conditions including recent (within the past year) or active suicidal ideation or behavior; or laboratory abnormalities that may increase the risk associated with study participation or study treatment administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the participant inappropriate for entry into this study. * Major surgery (eg, GI surgery, removal or biopsy of brain metastasis) within 8 weeks before first dose of study treatment. Complete wound healing from major surgery must have occurred 1 month before first dose and from minor surgery (eg, simple excision, tooth extraction) at least 28 days before first dose. Subjects with clinically relevant ongoing complications from prior surgery are not eligible.