The US Navy's 5th Fleet, which oversees the region, has not commented on the reports.
No members of the tanker crew were injured, added IRNA.
The report of Iranian oil tanker incident follows the September 14 attacks on two Saudi Arabian oil processing plants that knocked out more than half of the kingdom's crude oil output that caused a spike in oil prices.
The incident could also intensify tensions between Iran and the USA that began over a year ago when President Donald Trump unilaterally withdrew his country from the nuclear deal and imposed sanctions on Iran, crushing its economy.
There was no immediate acknowledgement from Saudi Arabia.
This attack follows a stand off between Iran, the United Kingdom and the USA over the positioning of oil tankers, an alleged attack on tankers, and a month on from the air strikes on Saudi oil facilities.
Tensions between Iran and Saudi Arabia reached a new peak last month when a major Saudi oil installation was struck.
According to the news service, the resulting explosions caused oil to leak into the Red Sea.
Yemen's Houthi group claimed responsibility for the attacks, but both Saudi Arabia and the United States have accused Iran of carrying them out, actions Tehran denies any involvement in.
The tanker, which was set ablaze, suffered heavy damage and crude had leaked after it was struck in the early morning about 60 miles (96 km) from Jeddah, Iranian media reported.
Refinitiv ship tracking data gave the Sabiti's last reported position on August 14 as off the southern coast of Iran in the Gulf.
Attacks on oil tankers in Gulf waters in June and July were also blamed on Iran.
It claimed the weapons used in the attacks were Iranian-made, but it stopped short of directly blaming its regional rival.