Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper or lightly grease.
Make cookies: Beat together white sugar, butter, and eggs in a large bowl using an electric mixer until smooth and creamy. Combine flour, cream of tartar, baking soda, and salt in a separate bowl; stir into creamed butter mixture until dough holds together.
Mix together white sugar and cinnamon in a small bowl until well combined.
Form dough into balls (about 2 teaspoons in each ball), then roll in cinnamon-sugar coating. Place dough balls about 2 inches apart onto the prepared baking sheet.
Bake in the preheated oven on the center rack for 7 minutes. Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.