Remove zest from tangerines with a vegetable peeler and save fruit for another use. Put zest in a 1-qt.* glass jar or decorative bottle. Pour in gin (through a funnel, if the bottle has a narrow opening).
Close jar tightly and put in a cool, dark place for 1 week.
Chill gin and serve cold; it will take on the color of the zest and will gradually intensify in flavor and get a little cloudy.
* You can use a smaller bottle, but the infusion will be stronger, so taste it occasionally and remove the zest when the liquor tastes the way you want.
Make ahead: Up to 3 months (1 year, strained), chilled.