The integration of Large Language Models (LLMs) into robotic control, including drones, has the potential to revolutionize autonomous systems. Research studies have demonstrated that LLMs can be leveraged to support robotic operations. However, when facing tasks with complex reasoning, concerns and challenges are raised about the reliability of solutions produced by LLMs. In this paper, we propose a prompt framework with enhanced reasoning to enable reliable LLM-driven control for drones. Our framework consists of novel technical components designed using Guidelines, Skill APIs, Constraints, and Examples, namely GSCE. GSCE is featured by its reliable and constraint-compliant code generation. We performed thorough experiments using GSCE for the control of drones with a wide level of task complexities. Our experiment results demonstrate that GSCE can significantly improve task success rates and completeness compared to baseline approaches, highlighting its potential for reliable LLM-driven autonomous drone systems.