Place the jalapeño on a sheet pan and broil for about 5 minutes, turning as needed, until blistered and blackened on all sides.
Add the blistered jalapeño, sugar, and water to a saucepan.
Bring to a boil until the sugar has completely dissolved.
Reduce the liquid by about one quarter.
Remove the saucepan from the heat and add the black tea bags.
Steep for 20 minutes.
Strain out the jalapeño and tea bags.
Stir in the apple cider vinegar.
Transfer to a glass pitcher or mason jars and chill before serving over ice.