This paper researches the teaching reform of the integration of sports and civic politics in the new era, and the addition of sports elements in civic politics education can achieve the mutual integration of the two. A personalized Civic and Political teaching model is constructed by combining the attention mechanism based on a recurrent neural network. Based on the personalized teaching model, a model of students’ academic ability in Civics and Politics is established. The EERNN model predicts the next Civics and Politics test scores and assists teachers in proactively intervening. The path of sports Civics integration is proposed from three aspects: increasing the implementation of sports Civics education, improving the awareness of Civics education of physical education teachers, and supervising the integration of students’ sports Civics thinking. Set up an experiment that compares the cognition of students in the experimental and control classes on health indicators and Civics elements. Analyze the student’s learning behaviors and the results after using the personalized recommendation Civics teaching model. The results of the experiment show that the students’ Civics elements of the seven dimensions improved after the experiment, respectively, by 3.05, 2.17, 3.79, 2.16, 2.67, 3.24, and 2.77. The Civics scores of the students in the experimental class increased from 113.89 to 123.48. The personalized learning model effectively enhanced the effectiveness of students’ civics learning.