Adapting word order from one language to another is a key problem in cross-lingual structured prediction. Current sentence encoders (e.g., RNN, Transformer with position embeddings) are usually word order sensitive. Even with uniform word form representations (MUSE, mBERT), word order discrepancies may hurt the adaptation of models. In this paper, we build structured prediction models with bag-of-words inputs, and introduce a new reordering module to organizing words following the source language order, which learns task-specific reordering strategies from a general-purpose order predictor model. Experiments on zero-shot cross-lingual dependency parsing, POS tagging, and morphological tagging show that our model can significantly improve target language performances, especially for languages that are distant from the source language.