WASHINGTON—A plea agreement by a former foreign-policy adviser to Donald Trump’s presidential campaign represents the most substantive link to date between the campaign and Russian attempts to influence the election through stolen emails, meetings and other measures.

The foreign-policy adviser, George Papadopoulos, acknowledged interacting with a professor who had close ties to the Kremlin and claimed that Russian officials could provide the Trump campaign with “dirt” on Hillary Clinton in the form of “thousands of emails,”...