AC rectifier and voltage regulator
A small 1:5 transformer will boost the voltage to the 1.5 to 2.5 V range, which will be enough to light up the LED. A current-limiting series resistor may or may not be needed, but just to be safe, make it 100 &Omega; to limit the current to 10 mA or so.

The LED can withstand the reverse voltage, so no other rectification should be necessary, but if you're really worried about it, just put an ordinary signal diode in parallel with the LED, pointing the other way.







simulate this circuit &ndash; Schematic created using CircuitLab