Differential gene expression in response to perturbations is mediated at least in part by changes in binding of transcription factors (TFs) and other proteins at specific genomic regions. Association of these cis-regulatory elements (CREs) with their target genes is a challenging task that is essential to address many biological and mechanistic questions. Many current approaches rely on chromatin conformation capture techniques or single-cell correlational methods to establish CRE-to-gene associations. These methods can be effective but have limitations, including resolution, gaps in detectable association distances, and cost. As an alternative, we have developed DegCre, a nonparametric method that evaluates correlations between measurements of perturbation-induced differential gene expression and differential regulatory signal at CREs to score possible CRE-to-gene associations. It has several unique features, including the ability to use any type of CRE activity measurement, yield probabilistic scores for CRE-to-gene pairs, and assess CRE-to-gene pairings across a wide range of sequence distances. We apply DegCre to six data sets, each using different perturbations and containing a variety of regulatory signal measurements, including chromatin openness, histone modifications, and TF occupancy. To test their efficacy, we compare DegCre associations to Hi-C loop calls and CRISPR-validated CRE-to-gene associations, establishing good performance by DegCre that is comparable or superior to competing methods. DegCre is a novel approach to the association of CREs to genes from a perturbation-differential perspective, with strengths that are complementary to existing approaches and allow for new insights into gene regulation.