lolwut? no. republics don't have to be democraTIC. regardless, the usa is a democratic (adj) republic (noun). not A democracy (noun).
and like i said, if we were a democracy, the senate would be an entirely redundant body.
"Representation in a republic may or may not be freely elected by the general citizenry. In many historical republics, representation has been based on personal status and the role of elections has been limited. This remains true today; among the
159 states that use the word "republic" in their official names as of 2017, and other states formally constituted as republics, are states that narrowly constrain both the right of representation and the process of election."