Combine garlic and artichoke hearts in a food processor; pulse for 30 seconds or until well chopped. With processor on, add the lemon juice, lemon zest, and olive oil, processing until smooth and well blended.
Stir in pepper and capers. Serve dip at room temperature or chilled with assorted crudités. Dip can be made 1 day in advance and stored in the fridge.