Deploying large language models (LLMs) with their extensive parameters and high memory demands challenges computational efficiency, particularly in fine-tuning for specific applications with limited resources. Techniques like Low-Rank Adaptation (LoRA) help by training a smaller, modifiable extension of the base model to reduce memory usage. However, combining quantization with LoRA, especially in low-bit scenarios, can lead to performance losses due to quantization errors. Our innovative Rank-Adaptive LoRA (RA-LoRA) addresses this by dynamically adjusting the adapter's rank using rank-subspace analysis, optimizing performance with fewer parameters. We tested RA-LoRA on state-of-the-art LLMs for 2-bit efficient fine-tuning, showing it can improve model accuracy with minimal trainable parameters, marking a leap forward in quantization-aware fine-tuning methods and highlighting the significance of rank dynamics in optimizing quantized LLMs.