Heat a skillet over medium heat and add the chorizo, cooking until it becomes crispy and releases fragrant smoky aroma, about 5-6 minutes. Drain excess fat and transfer the cooked chorizo to a plate.
Add oil to the same skillet if needed, then pour in beaten eggs. Stir gently with a spatula to scramble, cooking until eggs are just set and silky, about 2-3 minutes. Remove from heat.
Place tortillas on a clean surface and warm them briefly in a dry skillet or microwave until pliable, about 15-20 seconds.
Spread equal portions of chorizo and scrambled eggs onto the center of each tortilla, distributing evenly.
Fold the sides of the tortilla inwards, then roll the wrap tightly from one end to the other, sealing the filling inside.
Optional: Place the wraps seam-side down in a hot skillet for 1-2 minutes per side to lightly toast and secure the fold, adding a slight crisp to the exterior.
Remove the wraps from the skillet and slice in half diagonally. Serve immediately with hot sauce if desired for an extra kick.