Large-scale lithium-ion battery packs are widely adopted in systems such as electric vehicles and energy backup in power grids. Due to factors such as manufacturing difference and heterogeneous discharging conditions, cells in the battery pack may have different statuses, such as diverse voltage levels. This cell diversity is commonly known as the cell imbalance issue. For the charging of battery packs, the cell imbalance not only early on terminates the charging process before all cells are fully charged, but also leads to different desired charging currents among cells. In this paper, based on the advancement in reconfigurable battery systems, we demonstrate how to utilize system reconfigurability to mitigate the impact of cell imbalance on an efficient charging process. With the proposed reconfiguration-assisted charging (RAC), cells in the system are categorized according to their real-time voltages, and the charging process is performed in a category-by-category manner. To charge cells in a given category, a graph-based algorithm is presented to charge cells with their desired charging currents, respectively. We evaluate RAC through both experiments and simulations. The results demonstrate that the RAC increases the capacity charged into cells by about 25% and yields a dramatically reduced variance.