Because Renaissance Humanists told us so! Never mind the fact that the senate never wrote down their laws until a rebellion forced them to! How dare you question that we base our democracy on the Roman Senate (which was not elected)???

It was... sorta elected, in that you generally got in by having previously held any of several offices that were themselves generally elected (not very democratically by modern standards, but somewhat reasonably so compared to contemporary systems) or added to the body by an official (Censor) who was themselves elected.

Edited to add: I don't actually think it's unreasonable to take them at their word that the Roman Senate provided some meaningful inspiration for the US Senate, even if it ultimately wound up pretty different. That doesn't make it a good example of Roman innovation, though.