We present a method for using large language models (LLMs) to conduct public opinion polling with social media data. We sample accounts in the run-up to the 2020 US Presidential election based on recent posts related to the major-party candidates. An LLM extracts structured, survey-like data—including socio-demographic characteristics and voting behaviour—from these digital traces. We show that LLM labelling tends to agree with human raters with respect to characteristics of online users. The labelled social media accounts are mapped to a stratification frame, which facilitates MrP estimation of presidential vote share at the state level. We improve this model-based pre-election polling for severely biased online samples by introducing a bias-correction term. The end-to-end implementation takes unrepresentative, unstructured social media data as inputs and produces timely high-quality area-level estimates as outputs. This is artificially intelligent opinion polling. We show that our artificial intelligence (AI) polling estimates of the 2020 election are highly accurate, on par with estimates produced by state-level polling aggregators such as FiveThirtyEight, or from models fit to extremely expensive high-quality samples.