Anomaly detection is crucial to identify unusual patterns in various domains. In particular, continuous and rapid flow creates distinct challenges within streaming data. This paper introduces the Streaming Isolation Forest (SiForest), a novel algorithm that uses isolation principles and reservoir sampling to align the model with current data distributions. SiForest efficiently detects anomalies with minimal computational and memory requirements and dynamically updates its model using a subtree regrowing strategy. Empirical evaluation on twenty-three benchmark datasets demonstrates that SiForest outperforms eight state-of-the-art algorithms in terms of AUC-ROC scores, achieving greater precision and adaptability.