WASHINGTON—President Donald Trump has hired Joseph diGenova, a former U.S. attorney who was appointed independent counsel during the George H.W. Bush administration, to help represent him in the special counsel’s Russia investigation, a Trump lawyer said Monday.

Mr. diGenova, who has criticized the investigation into whether Trump associates colluded with Russia to skew the 2016 presidential election, will join Mr. Trump’s personal legal team, which is headed by John Dowd. Mr. Dowd drew criticism over the weekend after he...