Alexander was then selected by the Kansas City Royals in the sixth round of the 2010 Major League Baseball Draft and signed with them on June 11, 2010 for a $130,000 signing bonus.
He made his professional debut that season with the Idaho Falls Chukars of the Pioneer Baseball League, where he was 1–6 with a 5.73 ERA in 12 games (11 starts).
He subsequently missed the entire 2011 season due to left shoulder surgery and returned in 2012 to pitch in 10 games (six starts) for the Kane County Cougars of the Midwest League where he had a 2.55 ERA.

Alexander moved between three levels in the Royals farm system in 2013, with five games for the Lexington Legends of the South Atlantic League, 12 for the Wilmington Blue Rocks of the Carolina League and 24 for the Northwest Arkansas Naturals of the Texas League.
Overall, he was 5–1 with a 3.00 ERA and appeared exclusively out of the bullpen.
He did not allow a homerun all season and pitched had the second most innings pitched in the minor leagues (75) without a homer.
In 2015 he pitched in 35 games for the Naturals and 11 for the Omaha Storm Chasers of the Pacific Coast League.
He finished 2–4 with a 4.52 ERA in 67​²⁄₃ innings.
He pitched for the Gigantes del Cibao of the Dominican Winter League after the season and then returned to Omaha for 2015, where he was 2–3 with a 2.56 ERA in 63​¹⁄₃ innings over 41 games.
The Royals selected him as their Triple-A Pitcher of the Year.

Alexander was called up to the majors for the first time on September 1, 2015 and he made his MLB debut the following day against the Detroit Tigers.
He pitched a scoreless ninth inning, retiring two batters on groundouts and then striking out Nicholas Castellanos to end the game.
He pitched in six innings over four games for the Royals that season, allowing three runs on five hits with three strikeouts.

In 2016, he pitched in 22 games for Omaha and 17 for the Royals.
In the minors, he was 2–0 with a 3.00 ERA in 30 innings and in the majors he had a 3.32 ERA in 19 innings.
He made seven more appearances in the minors in 2017 but spent most of the year with the Royals, where he was 5–4 with a 2.48 ERA in 69 innings over 58 games.
He picked up his first MLB win on July 2 when he pitched two scoreless innings against the Minnesota Twins and his first save on August 22 against the Colorado Rockies.
Alexander was then selected by the Kansas City Royals in the sixth round of the 2010 Major League Baseball Draft and signed with them on June 11, 2010 for a $130,000 signing bonus. He made his professional debut that season with the Idaho Falls Chukars of the Pioneer Baseball League, where he was 1–6 with a 5.73 ERA in 12 games (11 starts). He subsequently missed the entire 2011 season due to left shoulder surgery and returned in 2012 to pitch in 10 games (six starts) for the Kane County Cougars of the Midwest League where he had a 2.55 ERA.
Alexander moved between three levels in the Royals farm system in 2013, with five games for the Lexington Legends of the South Atlantic League, 12 for the Wilmington Blue Rocks of the Carolina League and 24 for the Northwest Arkansas Naturals of the Texas League. Overall, he was 5–1 with a 3.00 ERA and appeared exclusively out of the bullpen. He did not allow a homerun all season and pitched had the second most innings pitched in the minor leagues (75) without a homer. In 2015 he pitched in 35 games for the Naturals and 11 for the Omaha Storm Chasers of the Pacific Coast League. He finished 2–4 with a 4.52 ERA in 67​²⁄₃ innings. He pitched for the Gigantes del Cibao of the Dominican Winter League after the season and then returned to Omaha for 2015, where he was 2–3 with a 2.56 ERA in 63​¹⁄₃ innings over 41 games. The Royals selected him as their Triple-A Pitcher of the Year.
Alexander was called up to the majors for the first time on September 1, 2015 and he made his MLB debut the following day against the Detroit Tigers. He pitched a scoreless ninth inning, retiring two batters on groundouts and then striking out Nicholas Castellanos to end the game. He pitched in six innings over four games for the Royals that season, allowing three runs on five hits with three strikeouts.
In 2016, he pitched in 22 games for Omaha and 17 for the Royals. In the minors, he was 2–0 with a 3.00 ERA in 30 innings and in the majors he had a 3.32 ERA in 19 innings. He made seven more appearances in the minors in 2017 but spent most of the year with the Royals, where he was 5–4 with a 2.48 ERA in 69 innings over 58 games. He picked up his first MLB win on July 2 when he pitched two scoreless innings against the Minnesota Twins and his first save on August 22 against the Colorado Rockies.
Scott Alexander