Lately, there has been growing interest in adapting vision-language models (VLMs) to image and third-person video classification due to their success in zero-shot recognition. However, the adaptation of these models to egocentric videos has been largely unexplored. To address this gap, we propose a simple yet effective cross-modal adaptation framework, which we call X-MIC. Using a video adapter, our pipeline learns to align frozen text embeddings to each egocentric video directly in the shared embedding space. Our novel adapter architecture retains and improves generalization of the pre-trained VLMs by disentangling learnable temporal modeling and frozen visual encoder. This results in an enhanced alignment of text embeddings to each egocentric video, leading to a significant improvement in cross-dataset generalization. We evaluate our approach on the Epic-Kitchens, Ego4D, and EGTEA datasets for fine-grained cross-dataset action generalization, demonstrating the effectiveness of our method.