Its mass goes down. Its mass goes up.
Work Step by Step
When an object loses electrons, it acquires a positive charge. Theoretically speaking, its mass decreases, by the mass of the electrons that went away. Practically speaking, this mass loss is far, far, far too small to measure for macroscopic objects. A similar argument shows that when an object gains electrons, it acquires a negative charge. Theoretically speaking, its mass increases, by the mass of the electrons that it picked up.