Special counsel Robert Mueller is bringing heightened scrutiny to Roger Stone, a longtime adviser to President Trump who claimed he had interactions with WikiLeaks founder Julian Assange during the 2016 presidential campaign.

On Thursday, Mr. Mueller subpoenaed the man Mr. Stone claims was his back channel to WikiLeaks throughout the campaign—New York comedian and radio personality Randy Credico. The subpoena was confirmed by Mr. Credico’s attorney, Martin Stolar.

Separately,...