You vote Democrat. You don't vote Democratic. You are therefore a Democrat voter.
You honestly can't see how that is plainly incorrect?
(I often wonder how many people who use this phrase incorrectly are deliberately trolling, or have simply been misled by those who are.)
Compare these two sentences:
"I voted Democrat for governor and senate."
"I voted Democratic for governor and senate."
We would use the first phrasing, at least in the wealthy, uberliberal parts of Massachusetts I frequent.
EDIT: How about this one:
"Democrat Deval Patrick for Governor" vs. "Democratic Deval Patrick for Governor"