This paper presents a modular AI agentic skill pipeline for automating subject indexing with Library of Congress Subject Headings (LCSH). Subject indexing - the process of analyzing a work's aboutness, selecting controlled vocabulary terms, and encoding them as MARC21 subject access fields - is one of the most time-consuming components of library cataloging. The system decomposes this process into four discrete, sequentially executed agent skills: conceptual analysis, quantitative filtering, authority validation, and MARC field synthesis. Each skill encodes domain knowledge drawn directly from Library of Congress Subject Headings Manual (SHM) instruction sheets and subject analysis theory. The pipeline was evaluated against a corpus of ten titles whose existing subject headings were captured from the Harvard Library bibliographic dataset (a snapshot of their Alma ILS). Results demonstrate strong conceptual alignment with professional subject indexing practice, with notable differences in specificity, subdivision practice, and the agent's adherence to the 2026 LC policy discontinuing form subdivisions in favor of LCGFT 655 fields.