In this paper, we introduce an innovative pre-training framework TP-Link, which aims to improve context-dependent Text-to-SQL Parsing by leveraging Linking information. This enhancement is achieved through better representation of both natural language utterances and the database schema, ultimately facilitating more effective text-to-SQL conversations. We present two novel pre-training objectives: (i) utterance linking prediction (ULP) task that models intricate syntactic relationships among natural language utterances in context-dependent text-to-SQL scenarios, and (ii) schema linking prediction (SLP) task that focuses on capturing fine-grained schema linking relationships between the utterances and the database schema. Extensive experiments demonstrate that our proposed TP-Link achieves state-of-the-art performance on two leading downstream benchmarks (i.e., SParC and CoSQL).