CycleGAN has been leveraged to synthesize a CT image from an available MR image after trained on unpaired data. Due to the lack of direct constraints between the synthetic and the input images, CycleGAN cannot guarantee structural consistency and often generates inaccurate mappings that shift the anatomy, which is highly undesirable for downstream clinical applications such as MRI-guided radiotherapy treatment planning and PET/MRI attenuation correction. In this paper, we propose a cycle-consistent and semantics-preserving generative adversarial network, referred as CycleSGAN, for unpaired MR-to-CT image synthesis. Our design features a novel and generic way to incorporate semantic information into CycleGAN. This is done by designing a pair of three-player games within the CycleGAN framework where each three-player game consists of one generator and two discriminators to formulate two distinct types of adversarial learning: appearance adversarial learning and structure adversarial learning. These two types of adversarial learning are alternately trained to ensure both realistic image synthesis and semantic structure preservation. Results on unpaired hip MR-to-CT image synthesis show that our method produces better synthetic CT images in both accuracy and visual quality as compared to other state-of-the-art (SOTA) unpaired MR-to-CT image synthesis methods.