Recent literature has suggested the potential of using large language models (LLMs) to make predictions for tabular tasks. However, LLMs have been shown to exhibit harmful social biases that reflect the stereotypes and inequalities present in the society. To this end, as well as the widespread use of tabular data in many high-stake applications, it is imperative to explore the following questions: what sources of information do LLMs draw upon when making predictions for tabular tasks; whether and to what extent are LLM predictions for tabular tasks influenced by social biases and stereotypes; and what are the consequential implications for fairness? Through a series of experiments, we delve into these questions and show that LLMs tend to inherit social biases from their training data which significantly impact their fairness in tabular prediction tasks. Furthermore, our investigations show that in the context of bias mitigation, though in-context learning and fine-tuning have a moderate effect, the fairness metric gap between different subgroups is still larger than that in traditional machine learning models, such as Random Forest and shallow Neural Networks. This observation emphasizes that the social biases are inherent within the LLMs themselves and inherited from their pre-training corpus, not only from the downstream task datasets. Besides, we demonstrate that label-flipping of in-context examples can significantly reduce biases, further highlighting the presence of inherent bias within LLMs.