The advent of online social networks has facilitated fast and wide spread of information. However, some users, especially members of minority groups, may be less likely to receive information spreading on the network, due to their disadvantaged network position. We study the optimization problem of adding new connections to a network to enhance fairness in information access among different demographic groups. We provide a concrete formulation of this problem where information access is measured in terms of resistance distance, {offering a new perspective that emphasizes global network structure and multi-path connectivity.} The problem is shown to be NP-hard. We propose a simple greedy algorithm which turns out to output accurate solutions, but its run time is cubic, which makes it undesirable for large networks. As our main technical contribution, we reduce its time complexity to linear, leveraging several novel approximation techniques. In addition to our theoretical findings, we also conduct an extensive set of experiments using both real-world and synthetic datasets. We demonstrate that our linear-time algorithm can produce accurate solutions for networks with millions of nodes.