In a 5- to 6-quart pan, combine wine, orange juice, and sugar. Bring to a boil over high heat, stirring often.
Add apricots, cover, and simmer gently until fruit is just tender when pierced, 3 to 5 minutes.
With a slotted spoon, transfer fruit to a bowl. Add ginger and orange peel to pan and return syrup to a boil. Boil, uncovered, until syrup is reduced to 1 1/4 cups, 10 to 12 minutes.
Let fruit and syrup cool until just slightly warm. If making ahead, combine syrup and apricots, cover, and chill up to 1 day.
Spoon fruit and syrup into bowls.