Cross-range scaling of the inverse synthetic aperture radar (ISAR) determines the real size of one cross-range unit, by which the geometry character of the target can be obtained. Considering the linear frequency modulation of the echo signal in slow-time domain, a new approach based on fractional Fourier transform (FrFT) is proposed for cross-range scaling. The approach estimates the chirp rate of the Doppler history and the target rotation vector according to the energy concentration property of the signal in the different fractional Fourier domain. The simulation results show that the algorithm is effective and accurate.