Rosario signed with the New York Mets as an international free agent in July 2012 for $1.75 million. It was the largest international signing bonus given by the Mets. Rosario made his professional debut in 2013 with the Kingsport Mets. He started 2014 with the Brooklyn Cyclones and was promoted to the Savannah Sand Gnats in September. Rosario was promoted to the Binghamton Mets on June 23, 2016. He was named to the 2016 MLB All Star Futures Game and went 1-for-2 in the game. Rosario ended 2016 with a .324 batting average, 5 home runs, and 71 RBIs.

The Mets added Rosario to their 40-man roster after the 2016 season. Rosario was assigned to the Las Vegas 51s of the Class AAA Pacific Coast League to start the 2017 season. In April 2017, Rosario was declared the top prospect in baseball by writer Keith Law. Rosario was named to the Triple-A All-Star Game and the All-Star Futures Game for 2017. Rosario earned Pacific Coast League All-Star honors as well as being awarded the 2017 PCL Rookie of the Year.

Rosario made his MLB debut on August 1, 2017 against the Colorado Rockies at Coors Field. In that game, Rosario recorded his first career Major League hit off of Scott Oberg. On August 11, 2017, Rosario hit his first career Major League home run off of Héctor Neris. He had his first career multi-home run game on May 20, 2018, hitting two home runs against the Arizona Diamondbacks.

On October 29, 2018, he was selected to play for the MLB All-Stars during the 2018 MLB Japan All-Star Series.

In 2019, he batted .287/.323/.432 with 15 home runs and 72 RBIs, and while he stole 19 bases he tied for the major league lead in caught stolen with 10. He had the lowest pull percentage of all NL batters (30.4%). On defense in 2019, he had -10 Defensive Runs Saved (DRS), the worst in the National League among qualifying shortstops. However, Rosario led the National League in singles.

On August 28, 2020, Rosario hit a walk-off home run against the New York Yankees at Yankee Stadium. The Mets were the home team because they were making up for a previously cancelled game. It was the first time a visiting player had hit a walk-off home run since Ed McKean hit one for the St. Louis Perfectos against the Cleveland Spiders in 1899.