A lawyer for Stephanie Clifford paid $25,000 on Monday to buy the rights to video footage of the former adult-film actress taking a lie-detector test about an alleged sexual encounter with President Donald Trump, the polygraph examiner who administered the test said.

The actress known professionally as Stormy Daniels took the test on May 19, 2011, in Las Vegas, according to a copy of the report by polygrapher Ronald Slay reviewed by The Wall Street Journal. She took the lie-detector test as part of an agreement to sell her...