Low-rank adaptation (LoRA) achieves parameter efficient fine-tuning for large language models (LLMs) by decomposing the model weight update into a pair of low-rank projection matrices. Yet, the memory overhead restricts it to scale up when the model size increases. We propose Randomized LoRA (RLoRA) which adopts Randomized Walsh-Hadamard Transform to achieve significant reduction in the size of trainable parameters compared to LoRA. At the same time, it allows a PAC-Bayes regularizer to be efficiently incorporated to improve generalization. We evaluate the effectiveness of RLoRA on LLMs RoBERTa, GPT-2 and LLaMA-7B using GLUE, E2E and math reasoning benchmarks. With a much lower memory requirement, RLoRA can give similar performance as the SOTA low-rank adaptation methods for these three tasks and significantly better performance under few-shot settings.