This paper introduces the Relational Connectivity Transformer (RCT), a novel Graph-Transformer model designed for predicting absolute and residual full-scale intelligence quotient (FSIQ), performance IQ (PIQ), and verbal IQ (VIQ) scores from resting-state functional magnetic resonance imaging (rs-fMRI) data. Early prediction of neurocognitive impairments via IQ scores may allow for timely intervention. To this end, our RCT model leverages a relation-learning strategy from paired sample data via a novel graph-based transformer framework. Through a comprehensive comparison with state-of-the-art approaches in a 5-fold cross-validation setup, our model demonstrated superior performance. Statistical analysis confirmed the significant improvement ( \(p<0.05\) ) in FSIQ prediction, strengthening the efficacy of the proposed method. This work marks the first application of a Graph-Transformer in predicting IQ scores using rs-fMRI, introducing a novel learning strategy and contributing to the ongoing efforts to enhance the accuracy and reliability of human intelligence predictions based on functional brain connectivity. The code is available in this GitHub repository.