Cloud radio access network (C-RAN) with centralized baseband processing is envisioned as a promising candidate for the next-generation wireless communication network. However, the joint processing gain of C-RAN is fundamentally constrained by the finite-capacity fronthaul links between the central unit (CU) where joint processing is implemented and distributed access points known as remote radio heads (RRHs). In this paper, we consider the downlink communication in a C-RAN with multi-antenna RRHs and single-antenna users, and investigate the joint RRH beamforming and user-RRH association problem to maximize the minimum signal-to-interference-plus-noise ratio (SINR) of all users subject to each RRH's individual fronthaul capacity constraint. The formulated problem is in general NP-hard due to the fronthaul capacity constraints and thus is difficult to be solved optimally. In this paper, we propose a new iterative method for this problem which decouples the design of beamforming and user association, where the number of users served by each RRH is iteratively reduced until the obtained beamforming and user association solution satisfies the fronthaul capacity constraints of all RRHs. A monotonic convergence is proved for the proposed algorithm, and it is shown by simulation that the algorithm achieves significant performance improvement over other heuristic solutions.