No, republic just means that the role of head of state isn't hereditary. Lots of dictatorships are republics, some democracies are as well. The actual political system of the USA is representative democracy (in theory at least).
The fact that these terms are so muddled in the minds of the average American is completely deliberate, because it makes it so much easier for them to subvert US democracy when people have been told that the US is not one.
A stick in a pile of flaming dogshit would have been a better president than Trump.