It doesn't have one.
A country only has a prime minister if it has a separate head of state and head of government. Then you have a president or monarch who is head of state, and a prime minister who is head of government.
But the US President does both jobs, so there is no need for a separate prime minister.
This is illustrated nicely by what happens when the POTUS makes a state visit to the UK. The invitation comes from the Queen, he is invited to stay at the palace, there will be a state banquet in his honour, they'll do all the usual ceremonial stuff like inspecting troops, blah blah blah. BUT the Queen does not do politics. Of course the President wants to talk politics, so a meeting with the Prime Minister has to be planned in as well. If the President wants to do that without all the ceremonial stuff, then it will be a head of government visit instead and the Queen won't be involved.