Do you mean from which modern country did the US acquire more territory than from other countries? (because you could argue that the whole land was taken from the native Americans, but they did not form one country at the time).
The biggest acquisition in the US history was the Louisiana purchase in 1803, when more than 800 000 sq miles where purchased: most of today's central US.
Two other significant purchases were Alaska (more than 600 000 miles) and the Mexican Cession (more than (500 000 sq miles).
