It's a failure of terms used in US politics. When we say "left" and "right" we pretty much exclusively are talking about their position in respect to one another as opposed to the actual policies the parties hold.

Republicans are much more "conservative" (right wing) than Democrats (liberals) are, so the Republicans are the right and the Democrats become the "left" as they aren't as conservative and therefore they are "to the left" of Republicans.

If you were to look at global definitions as to what it means to be a left wing party, Democrats really don't fit there.