Adequate exploitation of legume–rhizobia symbiosis for nitrogen fixation may help to alleviate the overuse of chemical nitrogen fertilizer and aid in sustainable agricultural development. However, controlling this beneficial interaction requires thorough characterization of the effects of soil rhizosphere microorganisms, especially core taxa, on the legume–rhizobia symbiosis. Here, we used Illumina sequencing to investigate the effects of cover crop (Raphanus sativus L. and Lolium perenne L.) residue on the rhizosphere soil microbial community and peanut nodulation ability. The results indicated that Raphanus sativus L. amendment (RS) significantly increased soil available phosphorus (AP) content and peanut nodulation ability, while the Lolium perenne L. amendment (LP) had no noticeable impact on peanut nodulation. LP and RS significantly elevated bacterial and rhizobial diversity, reduced fungal diversity, and shifted microbial community structure (bacteria, 14.7%, p = 0.001; rhizobia, 21.7%, p = 0.001; fungi, 25.5%, p = 0.001). Random forest analysis found that the core rhizosphere taxa, sharing similar ecological preferences, were the primary drivers of peanut nodulation. By least squares regression, soil AP content was found to be positively correlated with the relative abundance of key ecological clusters. Furthermore, RS was found to promote peanut nodulation by increasing the relative abundance of critical rhizosphere taxa. Overall, our findings emphasize that core microbial taxa might play an essential function in the modulation of legume nodulation and provide scientific evidence for the effective management of the plant microbiome.