Synthetic Aperture Radar (SAR) images are a valuable asset for a wide variety of tasks. In the last few years, many websites have been offering them for free in the form of easy to manage products, favoring their widespread diffusion and research work in the SAR field. The drawback of these opportunities is that such images might be exposed to forgeries and manipulations by malicious users, raising new concerns about their integrity and trustworthiness. Up to now, the multimedia forensics literature has proposed various techniques to localize manipulations in natural photographs, but the integrity assessment of SAR images was never investigated. This task poses new challenges, since SAR images are generated with a processing chain completely different from that of natural photographs. This implies that many forensics methods developed for natural images are not guaranteed to succeed. In this paper, we investigate the problem of amplitude SAR imagery splicing localization. Our goal is to localize regions of an amplitude SAR image that have been copied and pasted from another image, possibly undergoing some kind of editing in the process. To do so, we leverage a Convolutional Neural Network (CNN) to extract a fingerprint highlighting inconsistencies in the processing traces of the analyzed input. Then, we examine this fingerprint to produce a binary tampering mask indicating the pixel region under splicing attack. Results show that our proposed method, tailored to the nature of SAR signals, provides better performances than state-of-the-art forensic tools developed for natural images.