Hitherto statistical type inference systems rely thoroughly on supervised learning approaches, which require laborious manual effort to collect and label large amounts of data. Most Turing-complete imperative languages share similar control- and data-flow structures, which make it possible to transfer knowledge learned from one language to another. In this paper, we propose a cross-lingual transfer learning framework, PLATO, for statistical type inference, which allows us to leverage prior knowledge learned from the labeled dataset of one language and transfer it to the others, for example, Python to JavaScript, Java to JavaScript, etc. PLATO is powered by a novel kernelized attention mechanism to constrain the attention scope of the backbone Transformer model such that model is forced to base its prediction on commonly shared features among languages. In addition, we propose the syntax enhancement that augments the learning on the feature overlap among language domains. Furthermore, PLATO can also be used to improve the performance of the conventional supervised-based type inference by introducing cross-language augmentation, which enables the model to learn more general features across multiple languages. We evaluated PLATO under two settings: 1) under the cross-domain scenario that the target language data is not labelled or labelled partially, the results show that PLATO outperforms the state-of-the-art domain transfer techniques by a large margin, \eg, it improves the Python to TypeScript baseline by +14.6@EM, +18.6@weighted-F1, and 2) under the conventional mono-lingual supervised scenario, PLATO improves the Python baseline by +4.10@EM, +1.90@weighted-F1 with the introduction of the cross-lingual augmentation.