The site was unavailable during early afternoon, New York time, and according to media reports had been down for about an hour earlier in the day. Around 9 a.m. Friday there, the Anonymous Twitter account @YourAnonNews posted tweets saying the group had taken down the site.
The group also tweeted a link to a YouTube video in which it condemned Trump's recent statements calling for a temporary ban on Muslims entering the U.S. Anonymous said Trump's comments would help the Islamic State group recruit terrorists.
"Donald Trump, think twice before you speak anything," the video said.
Trump Tower, a 68-story, mixed-use building in midtown Manhattan, is the flagship property of the Trump Organization, the international real-estate company that Donald Trump leads as chairman and president.
Anonymous frequently hacks websites in the name of political causes and says it is engaged in a cyberwar against the Islamic State. It claims to have taken down thousands of Twitter accounts that support the group.
Earlier this week, Trump said the U.S. should bar all Muslims from entering the U.S. as a measure to prevent terror attacks, "until our country's representatives can figure out what's going on." The statements drew widespread condemnation in the U.S. and elsewhere but support from some right-leaning commentators. An NBC/Wall Street Journal poll found 57 percent of Americans opposed the idea.
Trump is the leading Republican candidate in the 2016 presidential election.