In this letter, we present the anisotropic Angular Radon Spectrum (ARS), a novel feature for global estimation of rotation in a two dimension space. ARS effectively describes collinearity of points and has the properties of translation-invariance and shift-rotation. We derive the analytical expression of ARS for Gaussian Mixture Models (GMM) representing point clouds where the Gaussian kernels have arbitrary covariances. Furthermore, we developed a preliminary procedure for simplification of GMM suitable for efficient computation of ARS. Rotation between point clouds is estimated by searching of maximum of correlation between their spectra. Correlation is efficiently computed from Fourier series expansion of ARS. Experiments on datasets of distorted object shapes, laser scans and on robotic mapping datasets assess the accuracy and robustness to noise in global rotation estimation.