Speech-to-SQL (S2SQL) aims to convert spoken questions into SQL queries given relational databases, which has been traditionally implemented in a cascaded manner while facing the following challenges: 1) model training is faced with the major issue of data scarcity, where limited parallel data is available; and 2) the systems should be robust enough to handle diverse out-of-domain speech samples that differ from the source data. In this work, we propose the first direct speech-to-SQL parsing model Wav2SQL which avoids error compounding across cascaded systems. Specifically, 1) to accelerate speech-driven SQL parsing research in the community, we release a large-scale and multi-speaker dataset MASpider; 2) leveraging the recent progress in the large-scale pre-training, we show that it alleviates the data scarcity issue and allow for direct speech-to-SQL parsing; and 3) we include the speech re-programming and gradient reversal classifier techniques to reduce acoustic variance and learned style-agnostic representation, improving generalization to unseen out-of-domain custom data. Experimental results demonstrate that Wav2SQL avoids error compounding and achieves state-of-the-art results by up to 2.5\% accuracy improvement over the baseline.