You have made two false statements in one sentence. Good job. We are not a democracy or a democratic republic. We are a Constitutional Republic.
As another poster so brilliantly noted, so was Nazi Germany a Republic, as well as the USSR.
We are a democratic form of government, like it or not. That's why there are uneven numbers of Justices on all Appeals Courts, and on SCOTUS, so that the majority will rule. That's also why the Vice President has the Constitutional power to cast the deciding vote in the case of the Senate voting 50-50; again, majority will rule. In State elections the majority of votes wins, democracy at work. They also count electoral votes in Presidential elections, and the candidate with the most electoral votes wins; majority rules, democracy at work. From city, county, state to federal government, majority rules. That's called democratic government.
Even when laws are written in our Constitution to protect minorities in America, those laws required a majority of votes to pass, so majority rules again, democracy prevails in the Republic. If you do not believe we are a democratic republic, then your argument is with men who are far brighter than I am, you are arguing with statesmen, historians, justices, Senators and Presidents, present and past, and of antiguity.
I have heard men like Rush Limbaugh, whom I listen to regularly and admire greatly say things about democracy like: "Democracy is mob rule". I don't know where Rush and others get the idea that a majority has to be a "mob". Can't a simple majority be a peacable, moral and just group? Why must they be symonomous with a "mob"? These are rhetorical questions of course.