Granger causality asks whether the past of one variable improves prediction of another while conditioning on the histories of the remaining variables. We introduce Granger-Causality Kolmogorov–Arnold Networks (GC-KAN), a framework for detecting such relationships in multivariate time series using target-specific Kolmogorov–Arnold Networks (KANs) to predict each variable from the joint lagged history of the system. The KAN representation provides lag-specific attribution and response diagnostics, allowing us to examine which inputs contribute to a prediction and how the fitted response depends on them. Proximal shrinkage selects a sparse set of predictive parents, while nested comparisons between models with and without each candidate source, calibrated using circular-shift surrogates, assess statistical support. We evaluate GC-KAN on vector-autoregressive and Lorenz–96 systems, a controlled response-recovery experiment, and NASA OMNI observations. GC-KAN achieves competitive parent recovery relative to component-wise multilayer perceptrons, an established neural approach to Granger-causality detection. In the controlled experiment, GC-KAN recovers an oscillatory predictive relationship more accurately than the component-wise multilayer perceptron, whereas the penalised spline additive model and the strongest neural additive model achieve closer fits. In the OMNI application, a model using measured physical variables directly retains the established north-south (B_z) asymmetry without engineered coupling proxies. Together, these results establish GC-KAN as a sparse Granger framework that can identify predictive parents and reveal nonlinear, lag-specific response structure beyond graph recovery and prediction accuracy alone.