Long-term coherent integration can significantly improve the ability to detect maneuvering targets by radar. Especially for weak targets, longer integration times are needed to improve. But for non-radially moving targets, the time-varying angle between target moving direction and radar line of sight will cause non-linear range migration (NLRM) and non-linear Doppler frequency migration (NLDFM) within long-time coherent processing, which precludes existing methods that ignore angle changes, and seriously degrades the performance of coherent integration. To solve this problem, an efficient method based on Radon Fourier transform (RFT) with modified variant angle model (ARFT) is proposed. In this method, a new parameter angle is introduced to optimize the target motion model, and the NLRM and NLDFM are eliminated by range-velocity-angle joint three-dimensional searching of ARFT. Compared with conventional algorithms, the proposed method can more accurately compensate for the NLRM and NLDFM, thus achieving better integration performance and detection probability for non-radial moving weak targets. Numerical simulations verify the effectiveness and advantages of the proposed method.