Adrian Morejon starred for his native Cuba internationally on the national team at the U-12 and U-15 levels. The 21 year old was a two-way phenom in the early days of his playing career.

During the final of the inaugural WBSC U-12 Baseball World Cup, Morejon made the highlight reel with a diving catch as a left fielder.

Cuba lost against the World Cup to host Chinese Taipei, 3-2. He was the starting pitcher in the semifinal against Venezuela, going 3.2 innings. Mailon Alonso earned the win pitching the final 2.1 innings.

Morejon was named the MVP of the WBSC U-15 Baseball World Cup 2014, played in Mazatlan, Mexico. He appeared in four games as a pitcher, starting three of them. He won the final against the United States, throwing a complete game. The left-hander touched that day the speed of 89 miles (143 kilometres) per hour.

The same year Morejon made his debut in Cuba's Serie Nacional. He pitched in six games for a total 24 innings of work.

He signed an US$ 11 million contract for the Major League Baseball (MLB) San Diego Padres in July 2016.

His professional career began in 2017 in the Padres Farm System. He was playing at Double-A Amarillo when he was named to the All-Star Futures Game in 2019. A few days later he made his MLB debut against the Chicago Cubs.

Morejon returned to the MLB club during the 2020 season and appeared in three postseason games for the Padres. He made his first start against the Los Angeles Dodgers on Friday, 9 October. His game lasted two innings. The Dodgers knocked out the Padres to advance to the National League Championship Series.