You don't have to have a formal "mixer" to mix either. The most fun "mixer" I went to was completely spontaneous. We were supposed to do fundraising at our football stadium but that got cancelled at the last minute. It was a huge game, so we still wanted to watch it. One of our sisters who was with us had a boyfriend in a fraternity, so a bunch of us girls showed up over there with food, had a cookout, and watched the game. It was only a few of us with a few of them, but random brothers kept showing up, so we met a ton of people. Apparently guys think girls who bring food over are cool, and they scheduled a mixer with our chapter soon after.
Maybe consider doing something smaller..find one of your sisters who's dating a guy in XYZ fraternity and see if you can drop in with something, go serenading, etc. It can't hurt.