Learning to ground natural language queries to target objects or regions in 3D point clouds is quite essential for 3D scene understanding. Nevertheless, existing 3D visual grounding approaches require a substantial number of bounding box annotations for text queries, which is time-consuming and labor-intensive to obtain. In this paper, we propose \textbf{3D-VLA}, a weakly supervised approach for \textbf{3D} visual grounding based on \textbf{V}isual \textbf{L}inguistic \textbf{A}lignment. Our 3D-VLA exploits the superior ability of current large-scale vision-language models (VLMs) on aligning the semantics between texts and 2D images, as well as the naturally existing correspondences between 2D images and 3D point clouds, and thus implicitly constructs correspondences between texts and 3D point clouds with no need for fine-grained box annotations in the training procedure. During the inference stage, the learned text-3D correspondence will help us ground the text queries to the 3D target objects even without 2D images. To the best of our knowledge, this is the first work to investigate 3D visual grounding in a weakly supervised manner by involving large scale vision-language models, and extensive experiments on ReferIt3D and ScanRefer datasets demonstrate that our 3D-VLA achieves comparable and even superior results over the fully supervised methods.