Artificial intelligence (AI) governance remains largely structured around risk mitigation and transparency rather than redistribution and repair. These approaches stabilize extractive data relations by preserving state and corporate control, leaving affected communities with limited recourse. We propose the Community Data Governance Stack (CDGS), a conceptual and infrastructural framework that treats governance as a first-class system design problem: specifying roles, rights, processes, and enforceable instruments through which communities can exercise meaningful control over AI data practices. Drawing on Indigenous Data Sovereignty, design justice, and labor scholarship, CDGS integrates sovereignty, refusal, fiduciary stewardship, benefit-sharing, and longitudinal oversight as coequal pillars of equitable governance. We outline implementable mechanisms—including community veto and withdrawal rights, fiduciary data trusts and cooperatives, benefit-sharing charters, and participatory review boards—that translate participation into co-governance rather than consultation. CDGS reframes evaluation beyond accuracy and compliance to assess whether AI systems deliver redistribution, redress, and repair through durable institutional and technical infrastructures.