Compressive sensing (CS) is successfully applied in inverse synthetic aperture radar (ISAR) imaging. But, as target rotation rate is not concerned in the CS-based imaging methods, the obtained image cannot be scaled in the cross-range dimension. Consequently, difficulties arise in extracting the target geometrical information from the CS ISAR image. But, target geometrical size is an important parameter in automatic radar target recognition. To remedy this problem, a joint ISAR imaging and cross-range scaling method is proposed. In the proposed method, an adaptive parametric dictionary, comprising chirp rate parameter, is used to represent the observed data. By minimizing the reconstruction error, sparsity-constrained optimization, combined with the chirp-rate parameter and target reflective coefficient, is established. To find a solution to the nonlinear and nonconvex optimization problem, an iterative procedure is developed. Finally, with the help of the chirp-rate, target rotation rate can be estimated by the least square method, and the ISAR image can be scaled in cross-range. Experimental results show that the proposed method can fit the observed data better than the method using a fixed Fourier dictionary. Besides, cross-range scaled ISAR images can be obtained with limited pulses.