Preheat oven to 400 degrees F (200 degrees C). Cut four 12x15-inch sheets of parchment paper. Fold each in half widthwise and reopen.
Mix rice, olives, chicken broth, orange juice, orange zest, salt, and pepper together in a bowl.
Spoon 3/4 cup of the rice mixture onto 1 side of each parchment rectangle, near the crease. Pile shrimp evenly over rice mixture. Drizzle 1 teaspoon olive oil over each pile of shrimp; lay 1 orange slice on top.
Fold empty half of parchment over shrimp filling and crimp edges together with overlapping folds to seal. Arrange packets close together on a sheet pan.
Roast on the center rack of the preheated oven until shrimp are tender and opaque, 15 to 17 minutes. Unfold 1 edge of the parchment, being careful to avoid steam, and look inside to check doneness.
Open packets carefully, being careful to avoid steam. Slide shrimp and rice mixture into bowls. Garnish with almonds and parsley.