In a small bowl, combine lukewarm water and food coloring. Set aside.
In a large mixing bowl, add flour and cream of tartar. Whisk to combine evenly, then make a well in the center and pour the colored water and oil.
Stir with a spoon at first, then, when it starts to be difficult to stir, use your hand to knead the playdough. The dough is sticky at first and dry as you go. If too sticky, add 1/2 tablespoon extra flour at a time.
This dough is not soft at first. It's normal if it looks tough and hard to knead. Keep kneading the dough for 2 minutes, pressing down, squeezing, and stretching until the color and flour are evenly distributed.
Set aside for 10 minutes at room temperature to relax the dough. The gluten will release from the flour, and the dough will soften with time.