In a medium mixing bowl, combine the softened cream cheese, shredded chicken, shredded cheddar, buffalo sauce, and ranch seasoning until evenly mixed.
Place a tortilla on a flat surface and spread about one quarter of the mixture into an even thin layer over the entire tortilla.
Starting at one edge, roll the tortilla snugly into a log and wrap tightly in plastic wrap. Repeat with remaining tortillas and filling.
Refrigerate the wrapped roll ups for 30 minutes to 1 hour, or until slightly firm for easier slicing.
Unwrap each roll, trim the ends to even them, and slice each roll into 1-inch pieces. Serve immediately or keep chilled until serving.