Anticipating the social impacts of a policy prior to implementation requires institutional consistency: multi-agent reasoning must remain aligned with the rules specified in policy documents. However, existing LLM-based multi-agent simulations struggle to maintain such fine-grained institutional rules when policy documents are provided only as prompt context. In this paper, we propose TIGRIS, a Theory-guided framework for Institutionally Grounded policy Impact Simulation. TIGRIS (1) constructs a structured policy knowledge graph from natural-language policy documents, using the Institutional Analysis and Development framework to define institutional positions and Institutional Grammar 2.0 to encode behavioral rules; and (2) instantiates actor nodes as persona agents while anchoring them to a Theory of Change framework to map the causal pathways of policy impacts. Evaluated across four AI talent development policies and three LLMs, TIGRIS achieves the lowest macro-average MAPE, indicating that theory-guided institutional grounding supports domain-aligned reasoning for policy impact analysis.