U.S. immigration law spans thousands of pages of official policy, federal regulations, and procedural guidance that change frequently and carry high stakes for petitioners who lack legal representation. We describe the construction of ImmigrationQA, a source-grounded question-answering dataset of 17,058 pairs across 13 immigration subdomains, and the fine-tuning of a Llama 3.2 3B Instruct model on that dataset using parameter-efficient LoRA. The corpus was assembled from 11 primary and secondary sources -- including the USCIS Policy Manual, 8 CFR, BIA precedent decisions, and community Q&A -- yielding 10,056 validated canonical documents and 18,308 text chunks. Structured QA pairs were generated from these chunks using Claude Sonnet 4.6 via five mode-specific prompts, with 22 pairs rejected for insufficient source-span overlap. The fine-tuned model was evaluated against a held-out split of 993 pairs using LLM-as-judge scoring on a 101-example stratified sample. The fine-tuned model scored a mean of 1.08/3.0 (16.8% fully correct; 101-example stratified eval) versus the Llama 3 8B base model at 0.85/3.0 (4% fully correct), a relative improvement of 27% in mean score; a zero-shot Claude Sonnet baseline scored 1.52/3.0 (25% fully correct). The fine-tuned model shows concentrated improvement in procedural subdomains (travel documents, adjustment of status, nonimmigrant visas) while remaining weak on complex legal reasoning and time-sensitive statistics. The full pipeline ran for approximately $29 in cloud compute. All artifacts -- dataset, model, code, and prompt templates -- are publicly released. The system is not a substitute for legal counsel and does not reflect regulatory changes after the corpus crawl date.