Before attempting this know that a 120VAC outlet rectified can reach much higher voltages DC, in the range of 170-210VDC.
This will supply 20 ma of DC current too a battery. If the current in this circuit is exceeded the LED will act as a fuse. This charger uses inexpensive parts and will supply dangerously high DC voltages with and without any load.
This circuit is supplied for educational purposes only. Working with live mains is always dangerous and should only be attempted by a trained professional.