In high-resolution radar imaging, the rotational motion of targets generally produces migration through resolution cells (MTRC) in inverse synthetic aperture radar (ISAR) images. Usually, it is a challenge to realize accurate MTRC correction on sparse aperture (SA) data, which tends to degrade the performance of translational motion compensation and SA-imaging. In this paper, we present a novel algorithm for high-resolution ISAR imaging and scaling from SA data, which effectively incorporates the translational motion phase error and MTRC corrections. In this algorithm, the ISAR image formation is converted into a sparsity-driven optimization via maximum a posterior (MAP) estimation, where the statistics of an ISAR image is modeled as complex Laplace distribution to provide a sparse prior. The translational motion phase error compensation and cross-range MTRC correction are modeled as joint range-invariant and range-variant phase error corrections in the range-compressed phase history domain. Our proposed imaging approach is performed by a two-step process: 1) the range-invariant and range-variant phase error estimations using a metric of minimum entropy are employed and solved by using a coordinate descent method to realize a coarse phase error correction. Meanwhile, the rotational motion can be obtained from the estimation of range-variant phase errors, which is used for ISAR scaling in the cross-range dimension; 2) under a two-dimensional (2-D) Fourier-based dictionary by involving the slant-range MTRC, joint MTRC-corrected ISAR imaging and accurate phase adjustment are realized by solving the sparsity-driven optimization with SA data, where the residual phase errors are treated as model error and removed to achieve a fine correction. Finally, some experiments based on simulated and measured data are performed to confirm the effectiveness of the proposed algorithm.