Robinson was one of 43 collegiate wide receivers to attend the NFL Scouting Combine in Indianapolis, Indiana. He performed all of the required combine drills and finished 26th among wide receivers in the 40-yard dash. On March 22, 2016, Robinson opted to attend Florida's pro day, along with Keanu Neal, Vernon Hargreaves, Jonathan Bullard, Jake McGee, Brian Poole, Kelvin Taylor, Alex McCalister, Antonio Morrison, and six other teammates. He chose to run all of the combine drills again and put up similar numbers from the combine. Scouts and team representatives from all 32 NFL teams attended, including Pittsburgh Steelers' General Manager Kevin Colbert, to scout Robinson as he performed positional drills. During the draft process, Robinson had private meetings and workouts with multiple teams, that Included the Philadelphia Eagles, Kansas City Chiefs, Oakland Raiders, and New York Jets. At the conclusion of the pre-draft process, Robinson was projected to be a fifth to seventh round draft pick by NFL draft experts and scouts. He was ranked the 23rd best wide receiver prospect in the draft by NFLDraftScout.com.
The Kansas City Chiefs selected Robinson in the fourth round (126th overall) of the 2016 NFL Draft. He was the 14th wide receiver selected in 2016.
On May 6, 2016, the Kansas City Chiefs signed Robinson to a four-year, $2.85 million contract that includes a signing bonus of $517,172.
He made his professional regular season debut in the Kansas City Chiefs' season-opening 33–27 victory over the San Diego Chargers. Robinson played in 16 games in 2016, but mainly appeared on special teams and finished without a statistic. After finishing 12–4, the Kansas City Chiefs received a playoff berth after finishing atop the AFC West. On January 15, 2017, Robinson appeared in his first career postseason game as the Chiefs lost 18-16 to the Pittsburgh Steelers in the AFC Divisional Round.