Although the prisoner is not druggged at first, later on in the story, his torturers do drug him, in order to inflict more torture upon him. After he has explored his prison and discovered the pit, he is exhausted and sleeps fitfully. Then, he describes,
"Upon arousing, I found by my side, as before, a loaf and a pitcher of water. A burning thirst consumed me, and I emptied the vessel at a draught. It must have been drugged; for scarcely had I drunk, before I became irresistibly drowsy."
This food that is laced with drugs only occurs after he has found the pit and failed to fall into it. His accusers know that their little pit scheme has failed, because after he falls, there is a brief flash of light into the chamber. We can assume that was one of his torturers, peeking into the prison to see if he had fallen into the pit. Once they realize that isn't going to work, they drug him and knock him out. After he wakes up from being drugged, he discovers that he is tied to a plank, and that there is a giant scythe slowly descending upon him.
So, his tormenters drugged him in order to try a different plan of action in regards to his demise. The pit was plan A, and when he didn't fall into it, they moved on to plan B. Why they didn't just go into the prison and man-handle him onto the plank is unknown; instead, they drugged him and tied him to it while he was unconscious. Perhaps they didn't want him to put up a fight, or didn't want him to know their identity, or maybe they just wanted to confuse and disorient him, and to add to his torture by having him discover, on his own, the gruesome death that awaited him at the blade of the scythe.
I hope that helped; good luck!
While Poe did create some narrators who were controlled by alcohol or other substances, the narrator of "The Pit and the Pendulum" does not seem to be under the influence of drugs. In the second paragraph of the story when the narrator confesses,
"I had swooned; but still will not say that all of consciousness was lost. What of it there remained I will not attempt to define, or even to describe; yet all was not lost. In the deepest slumber—no! In delirium—no! In a swoon—no! In death—no! even in the grave all is not lost,"
his delirium or hallucinations are not brought on by drugs but rather by the torture that he has undergone. Poe does not provide his readers with much background information for this narrator, but he does state that he is being tortured during and as a result of the Spanish Inquisition. Just as humans who have gone without food and water or who have endured some horrific event hallucinate and have difficulty distinguishing fantasy from reality, the narrator realizes that his memory and perception are not infallible because of his "sickness" or weakness.
What is interesting about the narrator of this story is that unlike many of Poe's other narrators who become increasingly unreliable as their stories progress, he actually becomes more lucid as "The Pit and the Pendulum" concludes, causing the reader to realize that much of what the narrator thought he might be hallucinating was actually reality for him.