In this paper, we introduce a secure wireless agentic AI network comprising one supervisor AI agent and multiple other AI agents to provision quality of service (QoS) for users' reasoning tasks while ensuring confidentiality of private knowledge and reasoning outcomes. Specifically, the supervisor AI agent can dynamically assign other AI agents to participate in cooperative reasoning, while the unselected AI agents act as friendly jammers to degrade the eavesdropper's interception performance. To extend the service duration of AI agents, an energy minimization problem is formulated that jointly optimizes AI agent selection, base station (BS) beamforming, and AI agent transmission power, subject to latency and reasoning accuracy constraints. To address the formulated problem, we propose two resource allocation schemes, ASC and LAW, which first decompose it into three sub-problems. Specifically, ASC optimizes each sub-problem iteratively using the proposed alternating direction method of multipliers (ADMM)-based algorithm, semi-definite relaxation (SDR), and successive convex approximation (SCA), while LAW tackles each sub-problem using the proposed large language model (LLM) optimizer within an agentic workflow. The experimental results show that the proposed solutions can reduce network energy consumption by up to 59.1% compared to other benchmark schemes. Furthermore, the proposed schemes are validated using a practical agentic AI system based on Qwen, demonstrating satisfactory reasoning accuracy across various public benchmarks.