In this article, we address the parameter estimation of micromotion targets in synthetic aperture radar (SAR), where scattering parameters and micromotion parameters of targets are coupled resulting in a nonlinear parameter estimation problem. The conventional methods address this nonlinear problem by matched filter, which are computationally expensive and of lower resolutions. In contrast, we address this problem by linearizing the forward model as a linear combination of elements of an over-complete dictionary. The essential idea of sparse signal representation models comes from the fact that SAR micromotion targets are sparsely distributed in the observation scene. Accordingly, we propose to jointly estimate the target micromotion and scattering parameters via a Bayesian approach with sparsity-inducing priors. In addition, we present a variational approximation framework for Bayesian computation. Numerical simulations demonstrate the proposed sparsity-inducing reconstruction method achieves higher resolution and better performance with smaller measures compared to conventional methods.