Neural implicit representations in Neural Radiance Fields (NeRF) have achieved impressive results in novel view synthesis and surface reconstruction tasks. However, their performance suffers under challenging scenarios with sparse input views. We present CorresNeRF, a method to leverage image correspondence priors computed by off-the-shelf methods to supervise the training of NeRF. These correspondence priors are first augmented and filtered with our adaptive algorithm. Then they are injected into the training process by adding loss terms on the reprojection error and depth error of the correspondence points. We evaluate our methods on novel view synthesis and surface reconstruction tasks with density-based and SDF-based neural implicit representations across different datasets. We show that this simple yet effective technique can be applied as a plug-and-play module to improve the performance of NeRF under sparse-view settings across different NeRF variants. Our experiments show that we outperform previous methods in both photometric and geometric metrics. The source code is available at https://github.com/yxlao/corres-nerf.