A user voting option is now available in the new extensions section of Challonge! settings. Facebook/Challonge! membership is required as usual, though I'm considering adding an anonymous voting option.
Here's a test bracket with very random entries if you'd like to check out the controls:
More to come, including module & mobile support, so look out for updates on this and additional extensions. Also, it's crunch time for March Madness, so if we get pools going again this year, you'll hear it here first. Though, it'd be nice to predict any bracket, and that extensions section has plenty of vacancy...