Click-Through Rate (CTR) prediction is a critical task in recommendation systems, aiming to predict the probability of a user clicking on an advertisement or item. High-order combinatorial features, also known as cross features, can uncover useful interactions among the features to enhance CTR prediction performance. In this paper, we proposed Feature Crossing Attention Network (FCAN) with Field-augmented Relational Tensors for CTR prediction. FCAN explores cross-layer interaction in which the feature representations in each intermediate layer serve as queries to interact with 1st-order feature embeddings as keys, which allows sequentially building up flexible nonlinear feature combinations while effectively controlling the order of interaction. Furthermore, we have extended the attention scheme from inner-product to hadamard-product based operator with field-augmented relational tensors, thus significantly enhancing the representation power of the learned interactions. Extensive experiments on four widely used real-world benchmark datasets demonstrate that our proposed method achieves superior performance.