Academic citation integrity faces persistent challenges, with research indicating 20% of citations contain errors and manual verification requiring months of expert time. This paper presents a novel AI-powered methodology for systematic, comprehensive reference auditing using agentic AI with tool-use capabilities. We develop a zero-assumption verification protocol that independently validates every reference against multiple academic databases (Semantic Scholar, Google Scholar, CrossRef) without assuming any citation is correct. The methodology was validated across 30 academic documents (2,581 references) spanning undergraduate projects to doctoral theses and peer-reviewed publications. Results demonstrate 91.7% average verification rate on published PLOS papers, with successful detection of fabricated references, retracted articles, orphan citations, and predatory journals. Time efficiency improved dramatically: 90-minute audits for 916-reference doctoral theses versus months of manual review. The system achieved <0.5% false positive rate while identifying critical issues manual review might miss. This work establishes the first validated AI-agent methodology for academic citation integrity, demonstrating practical applicability for supervisors, students, and institutional quality assurance.