Automatic Modulation Classification (AMC), as a crucial technique in modern non-cooperative communication networks, plays a key role in various civil and military applications. However, existing AMC methods usually are complicated and can work in batch mode only due to their high computational complexity. This paper introduces a new online AMC scheme based on Isolation Distributional Kernel. Our method stands out in two aspects. Firstly, it is the first proposal to represent baseband signals using a distributional kernel. Secondly, it introduces a pioneering AMC technique that works well in online settings under realistic time-varying channel conditions. Through extensive experiments in online settings, we demonstrate the effectiveness of the proposed classifier. Our results indicate that the proposed approach outperforms existing baseline models, including two state-of-the-art deep learning classifiers. Moreover, it distinguishes itself as the first online classifier for AMC with linear time complexity, which marks a significant efficiency boost for real-time applications.