Satellite networks can provide a wider service range and lower delay than traditional terrestrial optical fiber networks. However, due to the bursty characteristic of the Internet traffic and the distributive feature of satellite links, traffic-intensive areas often suffer from link congestion while links in other areas are underutilized, i.e., the traffic imbalance problem in LEO satellite networks. In this paper, an ant colony optimization routing algorithm with window reduction for LEO satellite networks, ACORA-WR, is proposed to achieve load balancing. ACORA-WR limits the movement of the ant colony to a specific range and comprehensively considers the path distance, transmission direction, and link load to find a path with low delay and overhead. Simulation results verify that the proposed ACORA-WR scheme demonstrates high data delivery ratio and network throughput, while ensuring low average delay and network transmission overhead.