Well, that depends on your definition of corrupt.

As you probably know, the Election of 1824 relied on a vote in the House of Representatives, because there was no definite consensus on who should be president (no one received a majority of electoral votes, just pluralities).

Now, in theory, Jackson should've won. He received the largest number of electoral votes, and the most popular votes. However, pluralities don't win. Also, the view of America as a democracy was a lot different then; it's commonly argued that the President was not so much a representative of the people yet. Jackson was swept into office in 1828 when the idea gained a real foothold, but it hadn't quite caught yet that the president was the "People's President", so much.

Now, because there were 4 candidates, but only 3 could be put to voting in the House of Representatives, Henry Clay was removed from the pool (lowest vote numbers). Jackson, Crawford, and Adams were the ones in the pool. So what happened next is important, and the crux of the name "Corrupt Bargain".

Clay, who was Speaker of the House at the time, agreed to support Adams. Was that necessarily because he wanted what followed, which was the position of Secretary of State? Plausible, but not factually undeniable. Clay hated Jackson, and knew that Adams would've had the best shot at beating Jackson, so he supported him. However, regardless of whether it was "corrupt" in the sense that Clay was taking a position that was supposed to be the best path to the presidency (essentially, he figured, leading him to be the next president), it was not illegal. There was nothing against the law about it. It was simply a deal of sorts, or an expression of appreciation.

What matters, though, is not whether or not it was a corrupt bargain in reality, but how it appeared. We may never know for sure if it was corruption and power-hunger that led to Clay supporting Adams, or just his general hate for Jackson, but the result is the same; the narrative of it being a corrupt bargain caught hold extensively throughout the United States, and it helped lead Jackson to power and a win in 1828. And regardless, Clay supported the candidate he personally preferred, rather than the one that got the largest plurality. So yeah, whether or not it was really a power-hungry grab (which most people think it was, but I don't think we'll ever be 100% sure, but it was made a rumor before Adams even offered Clay the job that it was a corrupt bargain), it was definitely not a decision motivated by the will of the people (because that was unclear), and it was definitely characterized and believed to be corrupt, which was as important as it actually being corrupt anyways.

We don't know what was said between Clay and Adams. Most historians doubt that there was anything explicitly stated that Clay would back Adams in return for the Secretary of state position. Moreover despite Clay's frequent opposition during the Monroe administration, Adams was clearly the candidate best aligned with Clay's own political values. Really the decision wasn't so much corrupt as a stupid mistake on Clay's part.