Rodman ranked No. 1 on the magazine's third annual list. The 52-year-old has visited Kim Jong Un in North Korea. GQ called him a "Q-list celebrity willing to commit borderline treason just to hang out with a dictator who himself aspires to be a Q-list celebrity."
Rodman said this week that he is preparing to return to North Korea late next month for an exhibition basketball tour.
Dean, who made headlines this year after she admitted to having used the N-word to describe black employees, came in at No. 2 on the list behind Rodman, while former sexting U.S. Rep. Anthony Weiner took the No. 3 spot.
"He's the saddest lecher in American politics, and that's saying something, because they're all lechers," the magazine said.
Cyrus, whose twerking performance garnered attention at this year's MTV Video Music Awards, won the No. 6 position for "basically trying every inane strategy she could think of to rile up America's few remaining pearl clutchers." The magazine noted "what's sad is that it totally worked."
President Barack Obama also made the list, coming in at No. 17. The magazine said the president was included in the list because "nothing gets done."
Other celebrities deemed non-influential include Justin Bieber, Lady Gaga, Ryan Reynolds and Will Smith.
The Associated Press contributed to this report.