The text-to-SQL problem aims to translate natural language questions into SQL statements to ease the interaction between database systems and end users. Recently, Large Language Models (LLMs) have exhibited impressive capabilities in a variety of tasks, including text-to-SQL. While prior works have explored various strategies for prompting LLMs to generate SQL statements, they still fall short of fully harnessing the power of LLM due to the lack of (1) high-quality contextual information when constructing the prompts and (2) robust feedback mechanisms to correct translation errors. To address these challenges, we propose MageSQL, a text-to-SQL approach based on in-context learning over LLMs. MageSQL explores a suite of techniques that leverage the syntax and semantics of SQL queries to identify relevant few-shot demonstrations as context for prompting LLMs. In particular, we introduce a graph-based demonstration selection method -- the first of its kind in the text-to-SQL problem -- that leverages graph contrastive learning adapted with SQL-specific data augmentation strategies. Furthermore, an error correction module is proposed to detect and fix potential inaccuracies in the generated SQL query. We conduct comprehensive evaluations on several benchmarking datasets. The results show that our proposed methods outperform state-of-the-art methods by an obvious margin.