Recently, pre-trained programming language models such as CodeBERT have demonstrated substantial gains in code search tasks. Despite their success, they rely on the availability of huge parallel data for fine-tuning code-query mappings. This restricts their practicality in domain-specific languages that have relatively scarce and costly data. In this paper, we propose CDCS, a novel approach for domain-specific code search. CDCS employs a few-shot transfer learning framework where an initial representation model is pre-trained on a large corpus of common programming languages (e.g., Java, Python) and is further adapted to domain-specific languages such as SQL and Solidity. Unlike cross-language CodeBERT which directly fine-tunes models in the target language, CDCS employs a meta-learning algorithm named MAML to learn an initialized model that can be best reused for the domain-specific language. We evaluate the proposed approach on two domain-specific languages, namely, SQL and Solidity, with model transferred from two widely used languages (Python and Java). Our results show that CDCS significantly outperforms baseline models that directly fine-tune models in the domain-specific language.