One challenge of integrating speech input with large language models (LLMs) stems from the discrepancy between the continuous nature of audio data and the discrete token-based paradigm of LLMs. To mitigate this gap, we propose a method for integrating vector quantization (VQ) into LLM-based automatic speech recognition (ASR). Using the LLM embedding table as the VQ codebook, the VQ module aligns the continuous representations from the audio encoder with the discrete LLM inputs, enabling the LLM to operate on a discretized audio representation that better reflects the linguistic structure. We further create a soft "discretization" of the audio representation by updating the codebook and performing a weighted sum over the codebook embeddings. Empirical results demonstrate that our proposed method significantly improves upon the LLM-based ASR baseline, particularly in out-of-domain conditions. This work highlights the potential of soft discretization as a modality bridge in LLM-based ASR.