Australian snowboarder said she hoped to send a message to Russian president Vladimir Putin about homophobia after new legislation was passed in the country banning the promotion of homosexuality to minors.
The 21-year-old medal-hopeful she was concerned for the safety of LGBT people in Russia, and urged the government to change its position.
"I've seen many documentaries about Russia and some of the violence towards the LGBT community and it's sickening and it's sad," she said.
"It's Putin's country and he can do what he likes with the country, but what I'm worried about is the safety of the LGBT community.
"Obviously, there's a lot of violence, torturing - torturing to death almost - and I'm hoping to see change after these games."
Brockhoff is part of the campaign, which states on its website that "Russia's anti-LGBT discrimination is incompatible with the Olympic movement."
The Australian bobsleigh team will display a logo for the campaign on their sled during competition.