Defining the terms 1. Yes, we're a democracy (and a republic as well).

The American system of government is democratic. We are a democracy

There's an odd objection in some quarters that arises from time to time to calling the US a democracy. At other times, we're proud of it.  During World War One we became, for instance, the Arsenal of Democracy.  Not the Arsenal of Republics.

Here's the deal.

Let's define democracy.

Merriam-Webster states the following:

Definition of democracy

1a: government by the peopleespecially : rule of the majority

b: a government in which the supreme power is vested in the people and exercised by them directly or indirectly through a system of representation usually involving periodically held free elections

2: a political unit that has a democratic government

3capitalized : the principles and policies of the Democratic party in the U.S.from emancipation Republicanism to New Deal Democracy— C. M. Roberts

4: the common people especially when constituting the source of political authority

5: the absence of hereditary or arbitrary class distinctions or privileges

Some might say, well so what, but that's about as good of set of definitions as any.

Given as we're discussing, principally, the means of choosing our leaders, we can probably exclude topics 3, 4, and 5, for the most part.

That leaves categories 1 and 2.

Some people, on this topic, like to say "we're a republic, not a democracy".  That displays, however, an erroneous understanding of what a republic is.

Let's go to the same source.  It states:

Definition of republic

1a(1): a government having a chief of state who is not a monarch and who in modern times is usually a president

(2): a political unit (such as a nation) having such a form of government

b(1): a government in which supreme power resides in a body of citizens entitled to vote and is exercised by elected officers and representatives responsible to them and governing according to law

(2): a political unit (such as a nation) having such a form of government

c: a usually specified republican government of a political unitthe French Fourth Republic

2: a body of persons freely engaged in a specified activitythe republic of letters

3: a constituent political and territorial unit of the former nations of Czechoslovakia, the Soviet Union, or Yugoslavia

We can obviously exclude 2 and 3 here.

Categories 1(a)(b) and (c) apply to the United States.

We choose our national legislature through democratic means.  We vote for them.  That makes us a democratic republic.

We're a democracy and a republic, just as the United Kingdom is a parliamentary democracy.

The United States has always been a democracy, but over time, its democratic nature has expanded enormously.  Only men could vote originally.  Indeed, in some colonies only propertied men could vote.  Native Americans and the enslaved couldn't vote, no matter where they were born, either.  Now all of this is in the past, and the voting age is 18, which it was not originally.

Also, we directly elect Senators, which was at one time not the case.  They were originally chosen by State Legislatures, although some case can be made that this might have worked better than the current system.

Operating against this, as the government has expanded enormously, certain legislative functions have been turned over to regulatory bodies, which do not function democratically, although they are required to take public input for their decisions.  And the Court started acting extra judicially in the 20th Century, which isn't democratic.  Both of these things have recently been scaled back, which has been a subject of controversy.

And we're not a "pure democracy".  No modern nation is.  A pure democracy is one in which the citizens vote on everything.  Examples of that are rare, with only ancient Athens coming to mind.  A pure democracy wouldn't work, for obvious reasons, for any sizable nation, or perhaps any modern nation of any type.

Before closing, we should note that we're a federal republic.  I.e, a system that brings in regions into the larger government.  So, once again, our national legislature is based upon regions, i.e., states.  We're not the only nation to have such an arrangement, by any means. Many do, and the varieties of that vary enormously.

Before we depart, the United States has traditionally been a "Liberal Democracy", which doesn't mean what it might at first seem to mean.  The Collins Dictionary defines a Liberal Democracy as follows:

a democracy based on the recognition of individual rights and freedoms, in which decisions from direct or representative processes prevail in many policy areas

Pretty broad, but other definitions get quite lengthy.

Recently we wrote on Illiberal Democracy.  Wikipedia defines Illiberal democracy as the following:

An illiberal democracy describes a governing system in which, although elections take place, citizens are cut off from knowledge about the activities of those who exercise real power because of the lack of civil liberties; thus it does not constitute an open society.

Proponents of illiberal democracy, and it does have proponents, would not define it that way. They'd probably define it as a system of government in which leaders are chosen democratically, but within an overarching set of agreed to principals and values which supersede and override democratic impulses, and control what can legitimately be debated.

Helpful?  Probably not much, but keeping in mind the deeper meaning of the terms is useful.

Basically, if people get to vote, and the vote determines the government, it's a democracy.  If people get to vote, but that doesn't matter, it isn't.