Asphalt rubber shows good road performance. However, the compatibility and aging problems of asphalt rubber limit its application. The improvement of the solubility of crumb rubber in asphalt was investigated in this research, and the mechanism of its aging effect on the rheological properties of activated asphalt rubber was studied. First, the crumb rubber was activated by using a sodium hypochlorite (NaClO) solution, and the pore characteristics and microstructure of the activated crumb rubber were analyzed. Second, the influence of the crumb rubber’s activation characteristics on the rheological properties of the asphalt rubber before and after aging was analyzed. Finally, the aging mechanism of the activated asphalt rubber was revealed at a microscopic level. The results showed that with the increase in the activation degree, the pore characteristics of the crumb rubber decreased first and then increased. The surface stacking structure of the crumb rubber increased, and a dense gel film gradually formed. The asphalt rubber prepared by the activated crumb rubber had better rheological properties and had a more significant effect under higher stress conditions. This may have been due to the activation of the crumb-rubber surface, forming oxygen-containing functional groups, which, in turn, increased the combination of the crumb rubber and the asphalt. In addition, the activation degree and aging effect of crumb rubber can reduce the large-particle-size molecule (LMS) content of activated asphalt rubber. There is a significant correlation between LMS content and rheological properties, and LMS content can be used to predict the rheological properties of asphalt rubber.