Maritime tracking website Vessel Finder shows Monday the United Kalavrvta is bound for the Texas port city of Galveston. Its last two port calls were in Gibraltar and Ceyhan, Turkey.
Kurdish oil is exported from the Turkish sea port of Ceyhan. At least three vessels have now left the Turkish port city loaded with oil from the Kurdish north of Iraq.
The federal government in Iraq considers sales of Kurdish oil illegal without its consent.
In June, U.S. State Department spokeswoman Jen Psaki said Washington was siding with Baghdad on the sale or export of Iraqi crude oil.
"We don't support the export or sale of oil, absent the appropriate approval of the federal Iraqi government," she said.
Both the Kurdish and federal governments have issued competing claims over the legality of oil exports.
A report from the U.S. Energy Department says Kurdish north of Iraq produces about 200,000 barrels of oil per day while southern Iraq produces 2.8 million bpd.