Hardware Trojans (HTs) are malicious alterations to the circuitry of integrated circuits (ICs), enabling unauthorized access, data theft, operational disruptions, or even physical harm. Detecting Hardware Trojans (HTD) is paramount for ensuring IC security. This paper introduces a novel Siamese neural network (SNN) framework for non-destructive HTD. The proposed framework can detect HTs by processing power side-channel signals without the need for a golden model of the IC. To obtain the best results, different neural network models such as Convolutional Neural Network (CNN), Gated Recurrent Unit (GRU), and Long Short-Term Memory (LSTM) are integrated individually with SNN. These models are trained on the extracted features from the Trojan Power & EM Side-Channel dataset. The results show that the Siamese LSTM model achieved the highest accuracy of 86.78%, followed by the Siamese GRU model with 83.59% accuracy and the Siamese CNN model with 73.54% accuracy. The comparison shows that of the proposed Siamese LSTM is a promising new approach for HTD and outperform the state-of-the-art methods.