Heat oven to 200°F. Line 2 cookie sheets with cooking parchment paper or foil. In large bowl, beat egg whites and cream of tartar with electric mixer on high speed until foamy. Gradually add sugar, 1 tablespoon at a time, beating until meringue is stiff and glossy. Beat in peppermint extract.
Fit large decorating bag with 1/4-inch star tip. With small brush, paint 3 to 4 evenly spaced stripes of food color on inside of decorating bag, from tip to upper edge. Carefully spoon meringue into bag. Pipe 2 1/2-inch candy canes onto paper-lined cookie sheets.
Bake about 1 hour or until dry but not brown.