The release of ChatGPT has uncovered a range of possibilities whereby large language models (LLMs) can substitute human intelligence. In this paper, we seek to understand whether ChatGPT has the potential to reproduce human-generated label annotations in social computing tasks. Such an achievement could significantly reduce the cost and complexity of social computing research. As such, we use ChatGPT to relabel five seminal datasets covering stance detection (2x), sentiment analysis, hate speech, and bot detection. Our results highlight that ChatGPT does have the potential to handle these data annotation tasks, although a number of challenges remain. ChatGPT obtains an average accuracy 0.609. Performance is highest for the sentiment analysis dataset, with ChatGPT correctly annotating 64.9% of tweets. Yet, we show that performance varies substantially across individual labels. We believe this work can open up new lines of analysis and act as a basis for future research into the exploitation of ChatGPT for human annotation tasks.