The previously reported photonics-based radar working with a large bandwidth has the advantages of realizing high-resolution imaging of targets with low velocity. However, the high velocity of a target will introduce Doppler dispersion to the echo signals, which severely deteriorates the imaging resolution. This problem becomes more noticeable as the bandwidth increases. In this paper, we propose a radar receiver based on a reconfigurable photonic fractional Fourier transformer (PFrFTer). The order of the PFrFTer can be reconstructed flexibly by changing the optical transform kernel. When the transform order matches the velocity of the target, the chirp echo signals behave as narrow impulses in the fractional Fourier domain, showing the range information with a high resolution. In the experiment, a PFrFTer is established and applied to process the echo signals with a bandwidth of 12 GHz. A lossless range resolution of 1.4 cm is obtained in range profiles and inverse synthetic aperture radar imaging for high-speed targets. This range resolution is much higher than that in the classical optical de-chirping receiver. These results demonstrate the PFrFTer is immune to the Doppler dispersion effect and is excellent for high-resolution imaging of high-speed target. The introduced technique would be of practical interest in the detection and recognition of targets.