Recent advancements in speech synthesis technologies have led to increasingly sophisticated spoofing attacks, posing significant challenges for automatic speaker verification systems. While systems based on self-supervised learning (SSL) models, particularly the XLSR-Conformer architecture, have demonstrated remarkable performance in synthetic speech detection, there remains room for architectural improvements. In this paper, we propose a novel approach that replaces the traditional Multi-Layer Perceptron (MLP) in the XLSR-Conformer model with a Kolmogorov-Arnold Network (KAN), a powerful universal approximator based on the Kolmogorov-Arnold representation theorem. Our experimental results on ASVspoof2021 demonstrate that the integration of KAN to XLSR-Conformer model can improve the performance by 60.55% relatively in Equal Error Rate (EER) LA and DF sets, further achieving 0.70% EER on the 21LA set. Besides, the proposed replacement is also robust to various SSL architectures. These findings suggest that incorporating KAN into SSL-based models is a promising direction for advances in synthetic speech detection.