Hardware Trojan (HT) is the primary concern for the semiconductor industries due to the involvement of external vendors in the integrated circuit (IC) design. Recently various Machine learning (ML) based HT detection techniques have been reported to automate the detection process. However, the major problem of applying ML algorithms in HT detection is the lack of standard large IC dataset, lack of relevant features, and class imbalance, which largely affects the detection performance. Therefore, this paper proposes a new HT detection technique, based on a few-shot learning and Deep Siamese CNN model that detects the HT from IC layout images. A new DCNN model-based architecture is proposed, which contains three convolutional and pooling layers that automatically extracts the invariant and relevant features from the IC images. Further, a new architecture based on the deep Siamese CNN (DSCNN) model is also proposed, which utilizes the same DCNN model twice and generates the similarity score based on the extracted image features for detection. The proposed DSCNN model is initially trained with a small synthetic ISCAS-85 dataset and then validated and tested with the unseen ISCAS-89 and Trust-Hub datasets, containing few samples per class. Finally, a new HT detection algorithm is proposed, which utilizes the two proposed models to perform the detection. Experimental results on synthetic ISCAS-89 and Trust-Hub datasets shows that the proposed technique achieves high detection accuracy in the presence of a few samples.