Rinse the shrimp and pat dry with a paper towel. Thinly slice the garlic. Coarsely chop the spinach.
Place the oil in a large non-stick skillet and heat over a medium-high heat. Reduce the heat to medium-low, add the garlic and cook, stirring frequently, until the garlic is golden, about 5 minutes. Watch closely so the garlic does not burn. Transfer the garlic to a small dish using a slotted spoon, leaving the oil in the skillet.
Raise the heat on the skillet to medium-high, add the shrimp, paprika, salt and cayenne and cook until the shrimp turns pink and is nearly cooked through, about 3 minutes. Stir in the spinach and return the garlic to the pan and cook until the shrimp is opaque throughout and the spinach is wilted, 1-2 minutes more.