Guiding users to actively expanding their online social circles is one of the primary strategies for enhancing user participation and growing online social networks. In this paper, we study the active friending problem which aims at providing users with the strategy for methodically sending invitations to successfully build a friendship with target users. We consider the prominent linear threshold model for the friending process and formulate the active friending problem as an optimization problem. The key observation is the relationship between the active friending problem and the minimum subset cover problem, based on which we present the first randomized algorithm with a data-independent approximation ratio and a controllable success probability for general graphs. The performance of the proposed algorithm is theoretically analyzed and supported by encouraging simulation results done on extensive datasets.