Heat the olive oil in a large pot over medium heat. Add the minced garlic and cook for 1 minute until fragrant.
Add the orzo to the pot and stir for 2 minutes to lightly toast it.
Pour in the chicken broth, lemon zest, salt, and black pepper. Bring the mixture to a boil, then reduce to a simmer.
Cook uncovered for 8 minutes, stirring occasionally, until the orzo is nearly tender and most of the liquid is absorbed.
Stir in the shrimp and fresh spinach. Cover the pot and cook for 4 to 5 minutes until the shrimp turn pink and opaque.
Remove from heat and stir in the lemon juice and chopped parsley. Serve with lemon wedges on the side.