Many fake news detection studies have achieved promising performance by extracting effective semantic and structure features from both content and propagation trees. However, it is challenging to apply them to practical situations, especially when using the trained propagation-based models to detect news with no propagation data. Towards this scenario, we study a new task named cold-start fake news detection, which aims to detect content-only samples with missing propagation. To achieve the task, we design a simple but effective Structure Adversarial Net (SAN) framework to learn transferable features from available propagation to boost the detection of content-only samples. SAN introduces a structure discriminator to estimate dissimilarities among learned features with and without propagation, and further learns structure-invariant features to enhance the generalization of existing propagation-based methods for content-only samples. We conduct qualitative and quantitative experiments on three datasets. Results show the challenge of the new task and the effectiveness of our SAN framework.