Deep learning (DL) has made notable progress in addressing complex radio access network control challenges that conventional analytic methods have struggled to solve. However, DL has shown limitations in solving constrained NP-hard problems often encountered in network optimization, such as those involving quality of service (QoS) or discrete variables like user indices. Current solutions rely on domain-specific architectures or heuristic techniques, and a general DL approach for constrained optimization remains undeveloped. Moreover, even minor changes in communication objectives demand time-consuming retraining, limiting their adaptability to dynamic environments where task objectives, constraints, environmental factors, and communication scenarios frequently change. To address these challenges, we propose a large language model for resource allocation optimizer (LLM-RAO), a novel approach that harnesses the capabilities of LLMs to address the complex resource allocation problem while adhering to QoS constraints. By employing a prompt-based tuning strategy to flexibly convey ever-changing task descriptions and requirements to the LLM, LLM-RAO demonstrates robust performance and seamless adaptability in dynamic environments without requiring extensive retraining. Simulation results reveal that LLM-RAO achieves up to a 40% performance enhancement compared to conventional DL methods and up to an $80$\% improvement over analytical approaches. Moreover, in scenarios with fluctuating communication objectives, LLM-RAO attains up to 2.9 times the performance of traditional DL-based networks.