Offline handwritten signature verification is a challenging pattern recognition task. One of the most significant limitations of the handwritten signature verification problem is inadequate data for training phases. Due to this limitation, deep learning methods that have obtained the state-of-the-art results in many areas achieve quite unsuccessful results when applied to signature verification. In this study, a new use of Cycle-GAN is proposed as a data augmentation method to address the inadequate data problem on signature verification. We also propose a novel signature verification system based on Caps-Net. The proposed data augmentation method is tested on four different convolutional neural network (CNN) methods, VGG16, VGG19, ResNet50, and DenseNet121, which are widely used in the literature. The method has provided a significant contribution to all mentioned CNN methods' success. The proposed data augmentation method has the best effect on the DenseNet121. We also tested our data augmentation method with the proposed signature verification system on two widely used databases: GPDS and MCYT. Compared to other studies, our verification system achieved the state-of-the-art results on MCYT database, while it reached the second-best verification result on GPDS.