WASHINGTON—A Russian woman accused of acting as an agent of Moscow pleaded guilty on Thursday to being part of a conspiracy to influence U.S. politics by becoming involved with the National Rifle Association and conservative activists.

Prosecutors allege that Maria Butina, 30, led a double life while in the U.S. on a student visa, covertly working with a top Russian banking official to develop back-channel relationships with conservative American politicians, as she tried to cultivate and infiltrate the influential gun-rights...