Question

Who has the power to levy tariffs

Answer 1

I think.
The President can levy tarrifs without the congress.

Answer 2

Tariffs are taxes that the government impose on imported goods in order to restrict imports by increasing the price of goods and services purchased from overseas and making them less attractive to consumers.  

Raising tariffs is usually the Congress’ job yet, for decades the Congress of the United States has been shifting the power to regulate on international trade to the executive branch (That means the president).