Answer:
The United States is not a direct democracy, in the sense of a country in which laws (and other government decisions) are made predominantly by majority vote. Some lawmaking is done this way, on the state and local levels, but it’s only a tiny fraction of all lawmaking. But we are a representative democracy, which is a form of democracy.
And indeed the American form of government has been called a “democracy” by leading American statesmen and legal commentators from the Framing on. It’s true that some Framing-era commentators made arguments that distinguished “democracy” and “republic”; see, for instance, The Federalist (No. 10), though even that first draws the distinction between “pure democracy” and a “republic,” only later just saying “democracy.” But even in that era, “representative democracy” was understood as a form of democracy, alongside “pure democracy