After being selected in the fourth round of the 2012 draft, Moscot made a quick rise to the big leagues. In 2015, after logging a 7–1 record with a 3.15 ERA for the AAA Louisville Bats, he was promoted to the majors. He made his major-league debut on June 5, at the age of 23. Moscot pitched 5 innings and allowed 4 runs, all coming in the first three innings, as he retired 13 of the last 15 batters he faced. In his next start, he won his first major-league game on June 10. Unfortunately, he suffered an injury to his non-throwing shoulder on a tag play, putting an end to the season after only three starts. He appeared in five games during the 2016 season.

He pitched for Team Israel in the 2019 European Championships and the 2020 Olympics qualifying tournament. He faced one batter in the Olympics opener against South Korea, but was removed when he suffered an elbow injury.