Research in linguistics shows that non-verbal cues, such as gestures, play a crucial role in spoken discourse. For example, speakers perform hand gestures to indicate topic shifts, helping listeners identify transitions in discourse. In this work, we investigate whether the joint modeling of gestures using human motion sequences and language can improve spoken discourse modeling in language models. To integrate gestures into language models, we first encode 3D human motion sequences into discrete gesture tokens using a VQ-VAE. These gesture token embeddings are then aligned with text embeddings through feature alignment, mapping them into the text embedding space. To evaluate the gesture-aligned language model on spoken discourse, we construct text infilling tasks targeting three key discourse cues grounded in linguistic research: discourse connectives, stance markers, and quantifiers. Results show that incorporating gestures enhances marker prediction accuracy across the three tasks, highlighting the complementary information that gestures can offer in modeling spoken discourse. We view this work as an initial step toward leveraging non-verbal cues to advance spoken language modeling in language models.