As AI systems evolve from single conversational agents to complex multi-agent architectures, a critical design dimension has been overlooked: how the social identity of individual agents shapes human behavior within the collaboration. This paper introduces the Agentic Social Affordance Framework (ASAF), a theoretical framework that extends Social Affordance theory into the context of multi-agent AI systems. We propose that agent identity design functions not merely as a user interface convention, but as a collaboration interface—structuring how users perceive, approach, and engage with each agent, and thereby influencing the quality of Human-Agent collaboration outcomes. Specifically, ASAF adopts the analytical separability of the social affordance layer and the engineering orchestration layer as a framing assumption—an organizing distinction that structures design analysis—rather than as a testable claim about effect-independence. The layers’ downstream effects can and do interact; the framing assumption is useful because it identifies a class of design considerations (cognitive posture, role-schema activation, oversight calibration) that is irreducible to engineering choices alone. ASAF comprises three mechanisms: Identity Signaling, Behavioral Priming, and Collaborative Governance, and specifies their boundary conditions through a four-tier Identity Signal Fidelity Spectrum and an individual-difference moderating variable (anthropomorphizing vs. instrumentalizing cognitive style). We situate ASAF in relation to existing affordance theory, the CASA paradigm, and classical multi-agent systems research, identifying a directional reversal: where classical MAS used roles, norms, and coordination to constrain autonomous agents, ASAF applies the same organizational vocabulary to structure the cognition and oversight of human operators who remain in the loop. ASAF positions social affordance design as a first-class design responsibility that engineering orchestration cannot subsume, with concrete implications for multi-agent system design. We outline directions for future empirical validation, including a factorial design for characterizing the empirical interaction surface between the social affordance and engineering orchestration layers.