President Donald Trump’s attorneys in the probe of Russian election interference are being funded in part through a Republican Party account with a handful of wealthy donors—including a billionaire investor, a property developer seeking U.S. government visas and a Ukrainian-born American who has made billions of dollars doing business with Russian oligarchs.

The Republican National Committee, through an account typically used for its own legal bills, paid more than $300,000 last month to help cover Mr. Trump’s private legal...