The growing scarcity of spectrum resources and rapid proliferation of wireless devices make efficient radio network management critical. While deep learning-enhanced Cognitive Radio Technology (CRT) provides promising solutions for tasks such as radio signal classification (RSC), denoising, and spectrum allocation, existing DL-based CRT frameworks are typically task-specific and lack scalability in diverse real-world applications. This limitation naturally leads to the exploration of Large Language Models (LLMs), whose exceptional cross-domain generalization capabilities offer new potential for advancing CRT. To bridge this gap, we propose RadioLLM, a novel framework that integrates Hybrid Prompt and Token Reprogramming (HPTR) for combining radio signal features with expert knowledge, and a Frequency-Attuned Fusion (FAF) module for enhanced high-frequency feature modeling. Extensive evaluations on multiple benchmark datasets demonstrate that RadioLLM achieves superior performance compared to existing baselines in the majority of testing scenarios.