There are several good recipes for making sugar cookies without baking soda. One of the easiest is Scotch shortbread, which is made with only three ingredients: butter; flour; and sugar. The second recipe for rolled sugar cookies contains baking powder but not baking soda.
Scotch Shortbread Cookies
Preheat the oven to 350 degrees F.
Mix 3/4 cup of butter and 1/4 cup of sugar thoroughly.
Work the 2 cups of flour in gradually by hand to make dough.
Roll out the dough to 1/3 to 1/2 inch thick.
Cut the dough into shapes with cookie cutters and place on the cookies on an ungreased baking sheet.
Bake 20 to 25 minutes.
Rolled Sugar Cookies
Stir together the flour, baking powder and 1/4 tsp. salt.
Beat the butter and shortening for 30 seconds. Then add the sugar and beat until fluffy.
Add the egg, milk and vanilla, and beat well.
Add the dry ingredients to the wet ingredients and mix well.
Cover and chill the dough in the refrigerator for at least three hours.
Preheat the oven to 375 degrees F.
Roll out the dough to a thickness of 1/8 inch. Cut it out with cookie cutters and place the cookies on an ungreased baking sheet.
Bake eight minutes or until golden brown.