We study a general formulation of program synthesis called syntax-guided synthesis(SyGuS) that concerns synthesizing a program that follows a given grammar and satisfies a given logical specification. Both the logical specification and the grammar have complex structures and can vary from task to task, posing significant challenges for learning across different tasks. Furthermore, training data is often unavailable for domain specific synthesis tasks. To address these challenges, we propose a meta-learning framework that learns a transferable policy from only weak supervision. Our framework consists of three components: 1) an encoder, which embeds both the logical specification and grammar at the same time using a graph neural network; 2) a grammar adaptive policy network which enables learning a transferable policy; and 3) a reinforcement learning algorithm that jointly trains the embedding and adaptive policy. We evaluate the framework on 214 cryptographic circuit synthesis tasks. It solves 141 of them in the out-of-box solver setting, significantly outperforming a similar search-based approach but without learning, which solves only 31. The result is comparable to two state-of-the-art classical synthesis engines, which solve 129 and 153 respectively. In the meta-solver setting, the framework can efficiently adapt to unseen tasks and achieves speedup ranging from 2x up to 100x.