If using wooden skewers, soak them in water for at least 30 minutes.
Pat the shrimp dry with paper towels.
In a large bowl, whisk together olive oil, lemon juice, garlic, lemon zest, Italian seasoning, paprika, salt, and black pepper.
Add the shrimp and toss until evenly coated.
Cover and refrigerate for 15 to 20 minutes.
Thread the shrimp onto skewers, leaving a small space between each shrimp.
Preheat the grill to medium-high heat.
Lightly oil the grill grates.
Place the shrimp skewers on the grill.
Cook for 2 to 3 minutes per side until the shrimp turn pink and opaque.
Remove from the grill and transfer to a serving platter.
Garnish with fresh parsley and lemon wedges before serving.