Murphy played college soccer for the Rutgers Scarlet Knights before starting her professional career with Montpellier in France.

[10] On January 18, 2018, National Women's Soccer League club Sky Blue FC selected Murphy with the 13th overall pick in the 2018 NWSL College Draft.

[8] The day after the draft, Murphy signed a professional contract with Montpellier HSC to play in France's Division 1 Féminine.

[5][17] She made her NWSL debut on May 27, 2019, making four saves in a 2–1 win against the North Carolina Courage, which marked the Reign's first victory over the team.

She was an unused substitute for Katelyn Rowland in the preseason NWSL Challenge Cup final on May 7, 2022, which the Courage won against the Washington Spirit.

[24] She started all but two games of the regular season and played in the Challenge Cup final on September 9, 2023, a 2–0 victory over Racing Louisville.

[30] Murphy received her first call-up to the senior United States women's national soccer team for a set of friendlies in June 2018 against China PR, but did not play.

[5][10][31] Murphy was again called up by United States head coach Vlatko Andonovski for the 2021 SheBelieves Cup, but did not appear in the tournament.

[5] Murphy was part of the senior United States team to travel to Australia for a pair of friendly matches in November 2021.

[5] In international friendlies from 2022 until April 7, 2023, in preparation for the 2023 FIFA Women's World Cup, Murphy and incumbent starter Alyssa Naeher each had 11 starting appearances for the United States.