Maintaining the correct fibre orientations and stacking sequence in carbon-fibre reinforced polymers (CFRP) during manufacture is essential for achieving the required mechanical properties of a component. This paper presents and evaluates a method for the rapid characterisation of the fibre orientations present in CFRP structures, and the differentiation of different stacking sequences, through the Radon-transform analysis of complex-valued eddy-current testing (ECT) inspection data. A high-frequency (20 MHz) eddy-current inspection system was used to obtain 2D scans of a range of CFRP samples of differing ply stacking sequences. The complex electrical impedance scan data was analysed using Radon-transform techniques to quickly and simply determine the dominant fibre orientations present in the structure. This method is compared to 2D-fast Fourier transform (2D-FFT) analysis of the same data and shown to give superior quantitative results with comparatively fewer computational steps and corrections. Further analysis is presented demonstrating and examining a method for preserving the complex information inherent within the eddy-current scan data during Radon-transform analysis. This investigation shows that the real and imaginary components of the ECT data encode information about the sacking sequence allowing the distinction between composites with different stacking structures. This new analysis technique could be used for in-process analysis of CFRP structures as a more accurate characterisation method, reducing the chance of costly manufacturing errors.