This paper reports a photonic chirp rates estimator for the piecewise linear frequency modulated waveforms (PLFMWs). The estimator is based on the photonic self-fractional Fourier transform (FrFT) by utilizing the input PLFMW as the transform kernel. In this way, the self-FrFT operation can be finished with short latency time and the chirp rates of all LFM sub-pulses can be retrieved according to their fractional frequencies. In experiment, the chirp rates estimation of a four-stage PLFMW is performed. The measurement range from -964.47 GHz/µs to 50.76 GHz/µs with resolution of 0.0518 GHz/µs is demonstrated for the experimental system. And the absolute measurement error within ±0.06 GHz/µs and the relative measurement error less than 2% is also obtained.