Warm sausage links according to package directions; set aside.
Meanwhile, in medium bow, beat together eggs and salsa until blended. Heat oil in 12-inch nonstick skillet over medium heat until just hot enough to sizzle drop of water. Pour egg mixture into skillet. As mixture begins to set, gently draw inverted pancake turner completely across bottom and sides of pan, forming large, soft curds. Gently stir in salsa con queso dip. Cook until not visible liquid egg remains. Do not stir constantly.
Divide egg mixture evenly among tortillas. Place one sausage link on each. Roll tortillas to form burritos. Serve with additional salsa, if desired.