In this letter, we propose a novel conjugate gradient (CG) adaptive filtering algorithm for online estimation of system responses that admit sparsity. Specifically, the Sparsity-promoting Conjugate Gradient (SCG) algorithm is developed based on iterative reweighting methods popular in the sparse signal recovery area. We propose an affine scaling transformation strategy within the reweighting framework, leading to an algorithm that allows the usage of a zero sparsity regularization coefficient. This enables SCG to leverage the sparsity of the system response if it already exists, while not compromising the optimization process. Simulation results show that SCG demonstrates improved convergence and steady-state properties over existing methods.