Preheat oven to 375 degrees F (190 degrees C). Grease cookie sheets.
Cream butter and sugar until very light and fluffy. Add egg and orange rind. Stir to blend.
In a separate bowl, combine flour, salt, baking powder and cinnamon. Add to butter mixture alternately with grated carrots. Mix to form a dough.
Drop by teaspoonfuls onto greased cookie sheet. Cookies will spread slightly. Bake for about 12 minutes or until cookies are lightly browned around the edges. Loosen cookies with spatula. Cool on rack.