Human beings are social creatures. We routinely reason about other agents, and a crucial component of this social reasoning is inferring people's goals as we learn about their actions. In many settings, we can perform intuitive but reliable goal inference from language descriptions of agents, actions, and the background environments. In this paper, we study this process of language driving and influencing social reasoning in a probabilistic goal inference domain. We propose a neuro-symbolic model that carries out goal inference from linguistic inputs of agent scenarios. The "neuro" part is a large language model (LLM) that translates language descriptions to code representations, and the "symbolic" part is a Bayesian inverse planning engine. To test our model, we design and run a human experiment on a linguistic goal inference task. Our model closely matches human response patterns and better predicts human judgements than using an LLM alone.