Grab a USB charger that supplies 5 V at least
> 20 mA. That will be nearly all of them. Cut off the end.
You now have a 5V power supply,
The resistor you need is calculated by the formula R < (5-3.8)/20e-3. This implies a resistor that's less than 60 ohms.
You can check the wattage needed by P = I^2*(R) and you yet 0.024 W; I'd use one of these
https://www.digikey.com/product-detail/en/ERG-1SJ560/P56W-1BK-ND/35855 The resistor will also act as a fuse.
You can go this route:
https://www.digikey.com/product-detail/en/ERG-1SJ560/P56W-1BK-ND/35855
and since the connector is 5.5/2.1 Digikey doesn't have a Jack, but your local radio Shack will.
With one resistor, you can only get the polarity wrong. If you use a 5V supply, if it doesn't work reverse the connections.
Your LED is marked somehow with the polarity. A pic would help.
Your circuit is a +power supply, resistor, Led (observe polarity) and back to - of power supply.
EDIT: Corrected per Reloadron. Not thinking straight today.