BuzzFeed says the study from UCLA researchers Colleen Carpinell and Kerri Johnson concludes Republican women are more likely to have what they call "stereotypically feminine facial features."
The study authors think that because the Republican platform advocates for traditional gender roles, women with more traditionally feminine appearances may gravitate toward the GOP. Interestingly, however, they found that Republican men actually had more feminine faces than Democratic men. This surprised Carpinella and Johnson, but they speculate that since governing is still seen as masculine in general, a slightly feminized appearance might not be an impediment to a Republican politician — he's already showing his masculinity by running for office in the first place. And Republicans may have an easier time getting away with slightly feminine faces than Democrats, since their political views are often seen as more masculine (cf. Arnold Schwarzenegger's claim that Democratic legislators were "girlie-men").
It's not clear if less-feminine women have a harder time making it in the Republican party (or if more-feminine women have difficulty being accepted by Democrats), or if people's physical appearances actually influence their political beliefs. Some research has found that political leanings can have genetic underpinnings — maybe the genes that affect liberalism or conservatism affect appearance as well. Or maybe the way women look as they grow up, and the way people respond to their appearance, influence how they vote later on. The less-principled in both parties are likely to spin this research in their favor — Democratic women are manly! Republican men are secret sissies! — but the reality is almost certainly more interesting.