Well, you need more specifics, what kind of ammunition, bb or .177 cal. (commonly confused), co2 or spring loaded firing mechanism, the guns FPS (if possible), and the small animal hypothetically intended to be killed.
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Yes it is possible but BB rifles are a poor choice for hunting. Because the BB does not deform on impact and will make the animal suffer. A head shot is best to kill the animal quickly. I would not hunt anything larger than a squirrel.