Reliable detection of surrounding objects is critical for the safe operation of connected automated vehicles (CAVs). However, inherent limitations such as the restricted perception range and occlusion effects compromise the reliability of single-vehicle perception systems in complex traffic environments. Collaborative perception has emerged as a promising approach by fusing sensor data from surrounding CAVs with diverse viewpoints, thereby improving environmental awareness. Although collaborative perception holds great promise, its performance is bottlenecked by wireless communication constraints, as unreliable and bandwidth-limited channels hinder the transmission of sensor data necessary for real-time perception. To address these challenges, this paper proposes SComCP, a novel task-oriented semantic communication framework for collaborative perception. Specifically, SComCP integrates an importance-aware feature selection network that selects and transmits semantic features most relevant to the perception task, significantly reducing communication overhead without sacrificing accuracy. Furthermore, we design a semantic codec network based on a joint source and channel coding (JSCC) architecture, which enables bidirectional transformation between semantic features and noise-tolerant channel symbols, thereby ensuring stable perception under adverse wireless conditions. Extensive experiments demonstrate the effectiveness of the proposed framework. In particular, compared to existing approaches, SComCP can maintain superior perception performance across various channel conditions, especially in low signal-to-noise ratio (SNR) scenarios. In addition, SComCP exhibits strong generalization capability, enabling the framework to maintain high performance across diverse channel conditions, even when trained with a specific channel model.