Rutledge was considered one of the top prospects for the
2019 Major League Baseball draft. He was selected by the
Washington Nationals with the 17th overall pick. He agreed to terms with the Nationals on June 17 for $3.45 million. He made his professional debut with the
Rookie-level Gulf Coast League Nationals before being promoted to the
Auburn Doubledays of the
Low–A New York–Penn League after one game. He was promoted to the
Hagerstown Suns of the
Single–A South Atlantic League in July, with whom he finished the year. Over ten starts between the three clubs, he went 2-0 with a 3.13 ERA, striking out 39 over innings. Rutledge did not play in a game in 2020 due to the cancellation of the minor league season because of the
COVID-19 pandemic. To begin the 2021 season, he was assigned to the
Wilmington Blue Rocks of the
High-A East. After pitching innings, in which he gave up 15
earned runs and 17 hits, he was placed on the
injured list with a shoulder injury. He was activated in July, and reassigned to the
Fredericksburg Nationals of the
Low-A East. He was placed back on the injured list in early August, and returned later that month. Over 22 innings pitched with Fredericksburg, Rutledge went 1-2 with a 5.32 ERA and 26 strikeouts. He was selected to play in the
Arizona Fall League for the
Surprise Saguaros after the season. Rutledge pitched 3⅓ innings in relief for the Saguaros in the championship game on November 20, 2021, versus the
Mesa Solar Sox, giving up two runs but striking out seven.
MLB Pipeline rated him as Surprise's top performer in the game, a 6–0 Mesa win. He returned to Fredericksburg to open the 2022 season. In 20 starts for Fredericksburg, he recorded a 8–6 record and 4.90 ERA with 99 strikeouts in innings pitched. On November 15, 2022, the Nationals added Rutledge to their
40-man roster to protect him from the
Rule 5 draft. He was optioned to the Double-A
Harrisburg Senators to begin the 2023 season. In 23 starts split between Harrisburg and the Triple–A
Rochester Red Wings, he accumulated an 8–4 record and 3.71 ERA with 106 strikeouts in 119 innings of work. On September 13, 2023, Rutledge was promoted to the major leagues for the first time. He faced the
Pittsburgh Pirates in his major league debut that same day, and took the loss. In 4 starts during his rookie campaign, he posted a 6.75 ERA with 12 strikeouts across 20 innings. Rutledge was optioned to Triple–A Rochester to begin the 2024 season. He made 3 appearances (1 start) for Washington in 2024, logging a 3.24 ERA with 9 strikeouts across innings pitched. Rutledge was again optioned to Triple-A Rochester to begin the 2025 season. He went on to make 63 relief appearances for the Nationals, compiling a 4-2 record and 5.77 ERA with 65 strikeouts across innings pitched. Rutledge was optioned to Triple-A Rochester to begin the 2026 season. He made one appearance for Washington on April 13, 2026, allowing seven runs on six hits with two strikeouts over innings pitched against the
Pittsburgh Pirates. On May 6, Rutledge was
designated for assignment by the Nationals. ==Pitching style==