Under the context of “double carbon” emission reduction, saline aquifer of sandstone is the most potential medium for carbon dioxide storage. The study of pore-structure characteristics determines the fluid migration and storage efficiency, which has great scientific significance. Fractal dimension is usually used to quantitatively characterize the distribution of sandstone pore structures in three-dimensional space. However, when studying the fractal dimension of sandstone pores in the past, the fractal dimension was calculated based on the characteristic values such as porosity, average pore radius, and average tortuosity, which could not well reflect the heterogeneity and arrangement of pore structures. Therefore, in this paper, pore structures of sandstone are generalized into capillaries with tortuosity. First, the image of rock slices is obtained by means of nuclear magnetic resonance imaging (MRI) technology, and the fractal dimension of pore distribution obtained by the box-counting dimension method is used. The fractal dimension of the pore distribution is the target parameter, and the fractal dimension of the tortuosity is calculated iteratively by combining the fractal scalar relationship between the number of capillaries and the pore size under different tortuosities. Compared with the traditional fractal dimension calculation method, the fractal dimension of tortuosity determined in this paper is larger, and the difference between different rock samples is more obvious, which can better reflect the heterogeneous characteristics of pore distribution.