For robots to understand human instructions and perform meaningful tasks in the near future, it is important to develop learned models that comprehend referential language to identify common objects in real-world 3D scenes. In this paper, we introduce a spatial-language model for a 3D visual grounding problem. Specifically, given a reconstructed 3D scene in the form of point clouds with 3D bounding boxes of potential object candidates, and a language utterance referring to a target object in the scene, our model successfully identifies the target object from a set of potential candidates. Specifically, LanguageRefer uses a transformer-based architecture that combines spatial embedding from bounding boxes with fine-tuned language embeddings from DistilBert to predict the target object. We show that it performs competitively on visio-linguistic datasets proposed by ReferIt3D. Further, we analyze its spatial reasoning task performance decoupled from perception noise, the accuracy of view-dependent utterances, and viewpoint annotations for potential robotics applications.