As an amateur, Robby Shelton played the 2015 Walker Cup team where he posted a record of 2–1. He also played on the US Palmer Cup team in 2014 and 2015.
At the 2015 Barbasol Championship on the PGA Tour, Robby finished tied for third. This was the highest finish by an amateur in a PGA Tour event since Phil Mickelson in 1991.
His first professional win was the Southern Hills Plantation on the Swing Thought Tour in 2017. Robby then followed it up with a win on the PGA Tour Canada later that year at the GolfBC Championship in British Colombia. This was en route to finishing second on the tour's money list, earning him a promotion to the Web.com Tour.
After taking home two victories on the Korn Ferry Tour in 2019 (Nashville Golf Open and Knoxville Open), Robby earned his PGA Tour membership. He ranked number 2 on the Korn Ferry Tour Regular Season points list, entering the 2019-20 season fourth in the final priority ranking.
In 2022, Robby won the BMW Charity Pro-Am presented by TD Synnex after entering a sudden-death playoff with Ben Griffin.
Achievements:
• T3 at the 2020 3M Open and made 13 of 24 cuts and recorded three top-10s
• Won twice on the 2019 Korn Ferry Tour (Nashville Golf Open and Knoxville Open)
• 2019 Robert Trent Jones Golf Trail Championship: Finished runner-up at 15-under 273
• T2 finish at the 2018 BMW Charity Pro-Am presented by SYNNEX Corporation
• Won his first career Mackenzie Tour title at the 2017 GolfBC Championship in British Colombia
• Finished No. 2 on the 2017 Mackenzie Tour – PGA TOUR Canada Order of Merit