The phrase sounds like it rises from back-country North American colloquialism. As commenter Verace notes, it means to make a disparaging appraisal, quite possibly in a humorous vein.
Its probable etymology is pugilistic: an attack on a statement or person (e.g., "Mrs. Clinton struck back at at Mr. Trump today.") Since a "poke" is a small, pointed blow, such as might be delivered at the point of a finger, the rhetorical diminution of the attack might serve as a mildly ironic understatement in service to humor.
The Dictionary of American Regional English might help to pin the origin down more specifically. My sense is that it's more mid-Atlantic or northern in origin, if only because "poke" is often a noun, meaning a sack or satchel, in parts of the American South.