The attack has not been verified but on its Twitter feed the group wrote: "Tango down - cia.gov - for the lulz".
A CIA spokesman told the Associated Press the agency was looking into the report. The American government's site does not contain any classified information.
The news follows a spate of recent hacks. Lulz Security claims responsibility for stealing the personal details of more than 100m users at Sony's PlayStation Network and Online Entertainment service. Lulz Security also claims to have attacked Nintendo, the US Senate site, and the site of the broadcaster PBS, after it aired a documentary Lulz considered critical of Wikileaks founder Julian Assange.
Last week Lulz Security warned the NHS its files were vulnerable to attack, although the hacking group said the NHS was not one of its targets. "While you aren't considered an enemy we did stumble upon several of your admin passwords," said the group on its Twitter feed.
Earlier this month US report claimed that hacking group Anonymous hacked into Iranian government servers and stolen more than 10,000 e-mail messages from the Ministry of Foreign Affairs.
This story was first published by Computer Weekly