Organizations increasingly allocate informational, evaluative, coordinative, and sometimes executive functions to algorithms, artificial intelligence systems, data objects, and robots. Yet organizational theory still often treats such technologies either as passive tools or as quasi-autonomous agents, obscuring how their influence is produced through relationships with human actors, organizational rules, and work arrangements. This original relational theory article develops a proposed Relational Theory of Nonhuman Agency that explains how nonhuman participation may become behaviorally consequential without assuming machine intentionality, personhood, or legitimate authority. The theory distinguishes functional participation from attributed authority, enacted dependence, trust calibration, and responsibility. It proposes that nonhuman actoric capacity becomes consequential only when organizational delegation and situated use convert technical capabilities into roles that shape attention, choice, evaluation, coordination, or action. The framework further proposes that attributed authority and enacted dependence are separable relational mechanisms: actors may defer to a system without depending on it, or depend on it without considering its outputs legitimate. These mechanisms are expected to interact with trust calibration, human discretion, task characteristics, opacity, expertise, and override conditions. The article identifies several forms of nonhuman organizational participation and develops testable relationships while preserving rival explanations grounded in conventional managerial authority, work design, incentives, and institutional context. The contribution is therefore conceptual rather than causal or validated: it specifies a relational architecture, explicit interpretation boundaries, and an agenda for future multilevel and longitudinal testing.