Are there common culinary uses for the addition of stearic acid?
Its main "culinary" use is as a binder or texture agent in "processed" foods.  You'll tend to find it in stuff like chewing gum, edible wax, and various candy elements like coatings.  

Aside from its natural occurrence (which, as noted in comments, comes in sorts of foods, but especially animal and vegetable oils and fats), it is also sometimes found in substances that are trying to mimic those oils or fats, like artificial butter flavoring, etc.

As a long-chain fatty acid, its solubility in water is limited, so it can't really be used as an "acid" in the way you tend to think about culinary stuff like vinegar or citric acid.  (And its effective pH would be way too high to do anything.)  The "fatty" part of the carbon chain also dominates the perceptual aspect of it, so it will taste more "fatty" than sour or acidic.