Mix rice, onion, curry powder, water, tortilla chips, vegetable oil, garlic, salt, and tarragon together in a bowl; add turkey and mix until thoroughly combined. Form mixture into 1-inch balls.
Preheat oven to 140 degrees F (60 degrees C).
Heat a large non-stick skillet over medium heat; add butter. Put about 12 balls in the melted butter and press each ball into a 1/2-inch thick patty using the back of a spatula. Cook until no longer pink in the center, 2 to 3 minutes per side. Transfer cooked patties to an oven-safe plate and keep warm in oven. Repeat with remaining balls, adding more butter as needed.