Preheat the oven to 425F. In a large bowl - or the bowl of a food processor - combine the flour, sugar, baking powder and salt. Add the butter and pulse or blend with a pastry blender or fork until combined, with some pieces of butter the size of a pea. (If you used a food processor, transfer the mixture to a bowl.)
Add the chai latte and stir until the dough comes together. Gather it into a ball and place on a parchment-lined sheet; pat into a circle an inch thick. Cut into 8 wedges with a knife and pull them apart from each other; if you like, sprinkle with coarse or vanilla sugar. Bake for 15-20 minutes, until deep golden.
Meanwhile, in a small bowl, whisk together the icing sugar and chai latte. Drizzle over the scones while they're still warm, or once they've cooled.