With the help of the dynamics model of the integration of AI and the management of college civic education, this paper investigates the integration of artificial intelligence and civic education in three directions: application specification, application design, and application practice. Using differential equations to represent the non-linear dynamics equations of the system and by means of differential solutions, the evolution mechanism of AI education application and integration is projected in this paper. The integration of AI and college civic education is explored through empirical analysis and comparative analysis. The results show that the average value of the comprehensive score of the three directions in the sample colleges and universities is 77.5828, which is in the bare integration stage, and the integration degree in the “formulation” path is the best, which is 85.698, and is in the complete integration stage. The students in the experimental class of the sample universities scored better than the control class without AI integration in civic education. There were no students with scores below 60, and there were 32 more students than the control class in the 90–100 segment.