The space-ground integrated network (SGIN) is an important direction of future network development and is expected to play an important role in edge computing for the Internet of Things (IoT). Through integration with an SGIN, IoT applications can provide services with long-distance and wide-coverage features. However, SGINs are typical large-scale and time-varying networks for which new network technologies, protocols, and applications must be rigorously evaluated and validated. Therefore, a reliable experimental platform is necessary for SGINs. This paper presents a cloud-based experimental platform for the SGIN context named SGIN-Stack. First, the architecture of SGIN-Stack, which combines the Systems Tool Kit (STK) and OpenStack, is described. Based on this architecture, a seamless linkage between OpenStack and STK is achieved to realize synchronous, dynamic, and real-time network emulation for an SGIN, and the dynamic differential compensation technology and a random number generation algorithm are applied to improve the emulation accuracy for satellite links. Finally, an emulation scenario is constructed that includes six space-based backbone nodes, sixty-six space-based access nodes, and a ground station. Based on this emulation scenario, experiments concerning the satellite link delays, bit error ratio (BER), and throughput are carried out to prove the high fidelity of our SGIN-Stack platform. Emulation experiments involving satellite orbital maneuvers and attitude adjustments show that SGIN-Stack can be used for dynamic and real-time SGIN emulation.