An efficient beamforming algorithm for large-scale phased arrays with lossy digital phase shifters is presented. This problem, which arises in microwave power transmission from solar power satellites, is to maximize the array gain in a desired direction with the gain loss of the phase shifters taken into account. In this paper the problem is first formulated as a discrete optimization problem, which is then decomposed into element-wise subproblems by the real rotation theorem. Based on this approach, a polynomial-time algorithm to solve the problem numerically is constructed and its effectiveness is verified by numerical simulations.