Congressional investigators are homing in on the connections between the 2016 presidential election and social-media giants Facebook and Twitter, a nexus that put Brad Parscale in charge of millions.

Brad Parscale was the Trump campaign’s digital director and his San Antonio company was its highest-paid vendor. Giles-Parscale drew nearly $88 million for about 18 months of work, according to Federal Election Commission disclosures, on top of an additional $4 million since Election Day, which included millions paid to Facebook and other social-media companies. As digital director, Mr. Parscale was responsible for creating and placing ads on social-media platforms such as Facebook, developing the campaign’s website and driving online fundraising efforts.

In July, Mr. Parscale agreed to an interview with the House Intelligence Committee, but later that month the panel postponed it. The committee hasn’t yet set a new date, and, according to a person familiar with the matter, Mr. Parscale hasn’t been contacted by the Senate Intelligence Committee or special counsel Robert Mueller, who, in addition to the congressional panels, is conducting a criminal probe into whether the Trump campaign and its associates colluded with Moscow.

Mr. Trump has denied any collusion by him or any associates, and Russia has said it didn’t meddle in the election.

Mr. Parscale denies any collusion with Moscow. “I am unaware of any Russian involvement in the digital and data operations of the 2016 Trump presidential campaign,” he said in a July statement.