Speech deepfake detection (SDD) is essential for maintaining trust in voice-driven technologies and digital media. Although recent SDD systems increasingly rely on self-supervised learning (SSL) representations that capture rich contextual information, complementary signal-driven acoustic features remain important for modeling fine-grained structural properties of speech. Most existing acoustic front ends are based on time-frequency representations, which do not fully exploit higher-order spectral dependencies inherent in speech signals. We introduce a cyclostationarity-inspired acoustic feature extraction framework for SDD based on spectral correlation density (SCD). The proposed features model periodic statistical structures in speech by capturing spectral correlations between frequency components. In particular, we propose temporally structured SCD features that characterize the evolution of spectral and cyclic-frequency components over time. The effectiveness and complementarity of the proposed features are evaluated using multiple countermeasure architectures, including convolutional neural networks, SSL-based embedding systems, and hybrid fusion models. Experiments on ASVspoof 2019 LA, ASVspoof 2021 DF, and ASVspoof 5 demonstrate that SCD-based features provide complementary discriminative information to SSL embeddings and conventional acoustic representations. In particular, fusion of SSL and SCD embeddings reduces the equal error rate on ASVspoof 2019 LA from $8.28\%$ to $0.98\%$, and yields consistent improvements on the challenging ASVspoof 5 dataset. The results highlight cyclostationary signal analysis as a theoretically grounded and effective front end for speech deepfake detection.