In this paper, we propose a parametric sparse recovery algorithm(SRA) applied to a radar signal model, based on the compressive sensing(CS), for the ISAR(Inverse Synthetic Aperture Radar) image reconstruction from an incomplete radar-cross-section(RCS) data and for the estimation of rotation rate of a target. As the SRA, the iteratively-reweighted-least-square(IRLS) is combined with the radar signal model including chirp components with unknown chirp rate in the cross-range direction. In addition, the particle swarm optimization(PSO) technique is considered for searching correct parameters related to the rotation rate. Therefore, the parametric SRA based on the IRLS can reconstruct ISAR image and estimate the rotation rate of a target efficiently, although there exists missing data in observed RCS data samples. The performance of the proposed method in terms of image entropy is also compared with that of the traditional interpolation methods for the incomplete RCS data.