Using a vegetable peeler, peel a (2-inch) strip of skin from the blood orange directly over a cocktail mixing glass to catch any oils; allow the peel to fall into the mixing glass.
Fill the mixing glass with ice.
Add the gin, Campari and sweet vermouth and stir with a cocktail spoon until very chilled, for at least 30 seconds.
Using a Julep strainer, strain the cocktail into an ice-filled rocks glass.
Peel another strip of skin from the blood orange and twist.
Rub the peel along the rim of the cup and drop into the cocktail; serve immediately.