Preheat the oven to 425 degrees and line a large baking sheet with parchment paper.
Place the red potato pieces in a large bowl with the corn pieces. Add the olive oil, Cajun seasoning, minced garlic, salt, and black pepper. Toss until everything is evenly coated.
Spread the potatoes and corn in a single layer on the prepared baking sheet. Roast for 20 minutes.
Remove the pan from the oven and add the shrimp to the same bowl. Toss quickly to coat the shrimp with any remaining seasoning.
Nestle the shrimp among the potatoes and corn on the baking sheet. Return the pan to the oven and roast for 8 to 10 minutes more, until the shrimp turn pink and opaque.
Remove from the oven and let the pan rest for 2 minutes before serving. Squeeze lemon wedges over the top and sprinkle with chopped parsley.