Robinson was born in Las Vegas, Nevada, and attended Silverado High School. He was drafted by the Rangers in the fourth round of the 2010 Major League Baseball Draft and began his professional career that season. Upon being drafted, one sources said, "he profiles as a potential solid starting corner outfielder at the Major League level." With the Arizona League Rangers in 2010, Robinson batted.286 with a.406 on-base percentage in 44 games. He split 2011 between the AZL Rangers and Spokane Indians, hitting a combined.200 with four home runs and 30 RBI in 51 games. For the Hickory Crawdads in 2012, Robinson batted.273 with a.409 on-base mark, hitting 13 home runs with 67 RBI, 10 steals and 86 walks in 123 games. He won his first Player of the Week honor that year. In 2013, Robinson batted.257 with eight home runs, 70 RBI and 10 stolen bases in 122 games for the Myrtle Beach Pelicans, earning another Player of the Week honor. With the Frisco RoughRiders and Round Rock Express in 2014, Robinson batted.198 with 12 home runs and 45 RBI in 96 games; in his first taste of Triple-A, he batted.304/.467/.522 with one home run and five RBI in eight games. He played for the RoughRiders and Express again in 2015, batting.235 with 21 home runs, 66 RBI, 16 stolen bases and 87 walks between them; again he performed well at Triple-A, batting.304 in 23 at-bats. He led the Texas League in home runs that year. He was a MiLB.com Organization All-Star in 2015 and earned another Player of the Week. In the offseason, he played for the Indios de Mayaguez in Puerto Rico. Going into 2016, Baseball America named him the #30 prospect in the Rangers system. He played in 2016 with Round Rock, for whom he batted.257/.350/.480 with 17 stolen bases.
Texas Rangers
Robinson made the Rangers' Opening Day roster in 2017. He made his major league debut on April 5. On June 25 he had his first major league hit, a home run, off Michael Pineda in a 7–6 Rangers victory over the New York Yankees at Yankee Stadium. With Texas in 2018, he batted.183/.288/.294 in 109 at bats, while with Round Rock he batted.303/.379/.569 in 211 at bats with 10 home runs.
St. Louis Cardinals
On December 11, 2018, the Rangers traded Robinson to the St. Louis Cardinals in exchange for Patrick Wisdom. He made St. Louis' 25-man roster to begin the 2019 season, but was optioned to the Memphis Redbirds and recalled twice during the season, totaling seven at bats with St. Louis for the season. With Memphis, he batted.265/.385/.423 with six home runs and 10 stolen bases in 189 at bats. In June, while with Memphis, Robinson was placed on the injured list, and subsequently underwent Tommy John surgery on his left elbow. On August 28, Robinson was released by St. Louis.
San Francisco Giants
On October 10, 2019, Robinson signed a minor league contract with the San Francisco Giants. In the major leagues, through 2019 he had played 28 games in center field, 24 games in left field, 23 games at third base, 15 games at second base, 7 games at shortstop, and 2 games in right field.
