Paraphrase generation plays an essential role in natural language process (NLP), and it has many downstream applications. However, training supervised paraphrase models requires many annotated paraphrase pairs, which are usually costly to obtain. On the other hand, the paraphrases generated by existing unsupervised approaches are usually syntactically similar to the source sentences and are limited in diversity. In this paper, we demonstrate that it is possible to generate syntactically various paraphrases without the need for annotated paraphrase pairs. We propose Syntactically controlled Paraphrase Generator (SynPG), an encoder-decoder based model that learns to disentangle the semantics and the syntax of a sentence from a collection of unannotated texts. The disentanglement enables SynPG to control the syntax of output paraphrases by manipulating the embedding in the syntactic space. Extensive experiments using automatic metrics and human evaluation show that SynPG performs better syntactic control than unsupervised baselines, while the quality of the generated paraphrases is competitive. We also demonstrate that the performance of SynPG is competitive or even better than supervised models when the unannotated data is large. Finally, we show that the syntactically controlled paraphrases generated by SynPG can be utilized for data augmentation to improve the robustness of NLP models.