Preheat the oven to 400 degrees F and line a rimmed baking sheet with parchment.
Put the sausage links on the prepared baking sheet and bake, turning once halfway through, until golden brown and cooked through, about 15 minutes; transfer to a paper towel to drain. Discard the parchment and reline the baking sheet with a new piece. Reduce the oven temperature to 375 degrees F.
Separate the cinnamon rolls; reserve the icing. Flatten each roll with your fingers to a 3 1/2- to 4-inch-long oval, then wrap it around a sausage link so the cinnamon-sugar side is on the outside. Arrange the wrapped sausages seam-side down and 1/2 inch apart in 2 rows of 8 on the prepared baking sheet.
Bake until the rolls are light golden brown, about 15 minutes. Let cool to room temperature.
Transfer the pigs-in-a-blanket to a serving dish, drizzle with the reserved icing and serve with the maple syrup on the side for dipping.
Copyright 2017 Television Food Network, G.P. All rights reserved.