Point set registration is significant for many applications such as recognition and reconstruction problems in computer science, and localization and mapping problems in robotic science. Traditional iterative closest point (ICP) algorithm is fast, hut it is only suitable for registration of rigid motions. Traditional affine ICP algorithm is fast enough and can match the shapes non-rigidly transformed, but it is not robust for noises and outliers. In this study, we propose a new affine ICP variant using correntropy criterion and point-to-line metric. Correntropy is a similarity measure between two random variables and it has outlier rejection property. By maximizing the objective function defined, the registration performance of Aline ICP is increased. The method proposed is also find transformation as fast as traditional Aline ICP algorithm. Experimental studies on 2D shapes show that our method is quite good in affine registration with noise and outliers in terms of accuracy and speed. The results are compared with state-of-the-art methods.