"We welcome constructive engagement with Attorney General Paxton," Shein said in a statement, adding that it will cooperate with the investigation. The company did not refer directly to Cotton's calls for a national probe.
The retailer is headquartered in Singapore but most of the goods sold on its platform are made in China, where it was founded.
In a letter to US Attorney General Pam Bondi on Monday, Cotton - senior Republican from Arkansas - said that millions of packages from China now sit in US warehouses after Washington changed its rules on low-cost shipments in August.
US President Donald Trump abolished the longstanding de minimis rule, a global tariff exemption widely used by buyers of low-cost goods.
The change subjected shipments to levies and stricter customs checks.
The new regulations gives the Department of Justice and Homeland Security a "golden opportunity" to act, said Cotton, a key ally of Trump and a vocal critic of China.
Designers and small American brands have accused Shein of systematically copying their original creations, often just days after launch, and selling them at a fraction of the price, he said.
