With the expanding demands for the space-air-ground integrated Internet of Things (IoT), the low-Earth orbit (LEO) satellite can be regarded as an important complement to IoT networks. Due to the transparency of satellite orbit information and the exposing nature of transmitting links, satellite-ground communication is extremely vulnerable to eavesdropping and jamming attacks. To establish a transmission link, the most crucial procedure was signal acquisition. Existing frequency hopping/direct sequence signal acquisition algorithms were either too time costing for the short visibility window of the LEO satellite or too resource costing for the LEO satellite devices. To alleviate this issue, we propose a novel differential coherent accumulation acquisition strategy for the LEO satellite-enabled IoT network to strike a balance between performance and complexity. It is also demonstrated that the proposed acquisition strategy is capable of achieving high-performance signal acquisition in the low-carrier-to-noise ratio and large dynamic regions. Moreover, we derive and simulate false alarm probability, detection probability, computational complexity, and mean square error of both the delay and Doppler factors in the additive white Gaussian noise channel. Numerical simulation results show that the proposed acquisition strategy improves the performance by 1.6 dB over the noncoherent accumulation strategy but at the expense of 0.43% complexity increase.