Depends on how you define the "movement." He has stated that he doesn't believe the US government was behind the attack but he does seem to believe in some kind of after-the-fact cover-up. He's also appeared on the radio show of 9/11 truther extraordinaire Alex Jones, though if that makes him a truther then Donald Trump and Gary Johnson also qualify.
Within a week of each other, two internet writers alleged recently that Castle is a 9/11 truther: Michael Harrington on Facebook, and Neil Stevens on Red State. Both of them pointed to a particular episode of Castle's podcast dedicated to the missing 28 pages of the 9/11 Commission Report. They also pointed out that he speaks credulously of other conspiracy theories, including making the statement in another episode of his podcast that both Barack Obama and Ted Cruz are "foreign born."
Another writer on Red State with the pseudonym Goldwater Conservative issued a defense of Castle's 28 pages podcast episode, saying that it did not espouse trutherism:
Essentially, Castle made three points. One, that the federal government was stonewalling efforts to have the pages released. Two, that the federal government was doing so to protect it's relationship with Saudi Arabia. Three, that the relationship primarily exists for financial reasons. All of those points are obviously true to any well-educated observer of politics. The United States supports the Islamic theocracy of Saudi Arabia for the same reason Russia supports the Islamic theocracy of Iran: it furthers each nation's economic interests, at least in theory.
Castle concluded his podcast by demanding that the pages be released, and stated that Saudi Arabia should face consequences if it turned out that they were implicated.
If Darrell Castle is a 9/11 truther for what he said above (he isn't), then so are many members of Congress who had the same questions. H.R. 14 and S.B. 1471 both urged the President to declassify the 28 pages, and the bills have 74 co-sponsors between them, many of whom publicly voiced the exact concerns and speculations that Castle raised in his podcast.
To conclude, at no point did Darrell Castle ever suggest that the United States planned or had foreknowledge of the 9/11 attacks. His discussion was perfectly reasonable, and his questioning of our flawed (and in the view of myself and many others: reprehensible) relationship with Saudi Arabia was refreshing to hear from a presidential candidate.
Castle himself responded to Harrington's write-up on Facebook:
Am I a Truther? I am always looking for the truth. Sometimes I am happy with what I find and sometimes not so much. Listen to my podcast "Twenty-eight Pages" and judge for yourself. I spend hours every week studying and preparing and producing the podcasts. I believe truth should be sought.
Stevens doubled down on his original assessment shortly thereafter:
I did listen to his podcast, and here's the conclusion I drew:
How about some Trutherism? Like Donald Trump, Castle suggests a massive 9/11 coverup, spinning a story that goes all the way back to the Bretton Woods deal, right up to the president day, including both Presidents Bush and Obama in his vast Saudi/9/11 conspiracy.
U.S. News interviewed Castle a few days later, and characterized his statements on the topic this way:
He says he believes the full story of the 9/11 attacks has not been told, though he stresses "I'm not a truther" and that he doesn't believe the U.S. government was behind the attacks.