In recent works, both sparsity-based methods as well as learning-based methods have proven to be successful in solving several challenging linear inverse problems. However, sparsity priors for natural signals and images suffer from poor discriminative capability, while learning-based methods seldom provide concrete theoretical guarantees. In this work, we advocate the idea of replacing hand-crafted priors, such as sparsity, with a Generative Adversarial Network (GAN) to solve linear inverse problems such as compressive sensing. In particular, we propose a projected gradient descent (PGD) algorithm for effective use of GAN priors for linear inverse problems, and also provide theoretical guarantees on the rate of convergence of this algorithm. Moreover, we show empirically that our algorithm demonstrates superior performance over an existing method of leveraging GANs for compressive sensing.