U.N. members agreed to place Iran on the crucial oversight panel during its general assembly meeting in September at the organization's headquarters in New York.
But given Iran's deep ties to Syrian President Bashar Assad and its armed support of the regime's forces, the U.N. decision "is outrageous and puts a fox in charge of the hen house," Rogers said in a statement.
"This is a county that has centrifuges actively spinning in an effort to obtain a nuclear weapon, the Michigan Republican said.
"Placing a patron state of Syria on this committee as the U.N. begins disarmament of Syria’s chemical weapons is a further blow to the credibility of the United Nations," Rogers added.
The U.N. deal is part of a Russian-brokered plan to disarm Assad's forces, who used chemical weapons against anti-government rebels fighting to topple the Syrian regime.
The deal staved off planned U.S. military strikes against targets inside Syria in retaliation for the chemical weapon attacks.
Along with Iran, Russia has been Syria's main international benefactor, providing weapons and military support to the regime's forces over the course of the 2 1/2-year civil war.
Tehran's new post on the council comes amid recent efforts by Iran to reach out to the United States and its allies, led by President Hassan Rouhani.
But Iran's continued sponsorship of Hezbollah and support to the Assad regime, as well as ongoing nuclear enrichment efforts, has cast doubt on Rouhani's diplomatic overtures to Washington.
"We need to approach the current diplomatic initiative with eyes wide open," Sens. John McCain (R-Ariz.), Lindsey Graham (R-S.C.) and Kelly Ayotte (R-N.H.) said in a statement in September.
"We are deeply skeptical about the real motivations behind Iran's charm offensive," they said.