This paper considers the design of beamforming matrices for multi-cell interference alignment (IA). Different from the existing centralized algorithms for coordinated IA, the focus here is on low-complexity distributed algorithms that are easy to implement on large networks. Towards this end, the rank-minimization form of the coordinated IA problem is formulated as a general-form consensus problem, that is solvable via a distributed alternating directions method of multipliers algorithm. The non-convexity of the original problem is overcome by utilizing a proximal update step. The proposed algorithm is flexible enough to allow delays and losses in the update process, while still being provably convergent to a stationary point. Simulations are carried out on a six-cell system, demonstrating the effectiveness of the proposed algorithm.