Interference alignment (IA) is a cooperative transmission strategy that improves spectral efficiency in high signal-to-noise ratio (SNR) environments, yet performs poorly in low-SNR scenarios. This limits IA's utility in cellular systems as it is ineffective in improving cell-edge data rates. Modern cellular architectures such as distributed antenna systems (DAS), however, promise to boost cell-edge SNR, creating the environment needed to realize practical IA gains. Existing IA solutions cannot be applied to DAS as they neglect the per-remote-radio power constraints imposed on distributed precoders. This paper considers two types of distributed antenna IA systems: ones with a limit on maximum per-radio power, and ones with a strict equality constraint on per-radio power. The rate-loss incurred by a simple power back-off strategy, used in systems with maximum power constraints, is characterized analytically. It is also shown that enforcing strict power constraints avoids such a rate-loss but negatively affects IA feasibility. For such systems, an IA algorithm is proposed and feasibility conditions are derived based on the concept of system properness. Finally, numerical results validate the analysis and demonstrate that IA and DAS can be successfully combined to mitigate inter-cell interference and improve performance for most mobile users, especially those at the cell-edge.