As almost $31 trillion has flowed into investment funds and strategies that emphasize good governance and socially responsible business practices, hedge funds have largely found themselves left out.

They are starting to find a way in. Nearly 30% of hedge funds say they are using environmental, social, and corporate governance considerations to inform investment decisions, according to Preqin research released this month—the first time the data provider put the question to hedge fund clients.

“The activity level relative to ESG...