Long-time coherent integration technique is one of the most important methods for the improvement of radar detection ability of a weak maneuvering target, whereas the integration performance may be greatly influenced by the across range unit (ARU) and Doppler frequency migration (DFM) effects. In this paper, a novel representation known as Radon-fractional Fourier transform (RFRFT) is proposed and investigated to solve the above problems simultaneously. It can not only eliminate the effect of DFM by selecting a proper rotation angle but also achieve long-time coherent integration without ARU effect. The RFRFT can be regarded as a special Doppler filter bank composed of filters with different rotation angles, which indicates a generalization of the traditional moving target detection (MTD) and FRFT methods. Some useful properties and the likelihood ratio test detector of RFRFT are derived for maneuvering target detection. Finally, numerical experiments of aerial target and marine target detection are carried out using simulated and real radar datasets. The results demonstrate that for integration gain and detection ability, the proposed method is superior to MTD, FRFT, and Radon-Fourier transform under low signal-to-clutter/noise ratio (SCR/SNR) environments. Moreover, the trajectory of target can be easily obtained via RFRFT as well.