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. Throughout his first training camp, he competed against Seantavius Jones, Mike Williams, Da'Ron Brown, Tyreek Hill, Mitch Mathews, and Kashif Moore for a backup wide receiver role. Head coach Andy Reid named him the fourth wide receiver on the depth chart to start the season, behind Jeremy Maclin, Albert Wilson, and Chris Conley. 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. The Chiefs opted to release wide receiver Jeremy Maclin during training camp and held an open competition for his vacant starting wide receiver role. Robinson competed against Chris Conley, Tyreek Hill, De'Anthony Thomas, Albert Wilson, and Kenny Cook. He was named the fifth wide receiver on the depth chart behind Conley, Hill, Wilson, and Thomas. On September 24, 2017, Robinson caught two passes for nine-yards during a 24–10 victory at the Los Angeles Chargers. He made his first career reception on a two-yard pass by quarterback Alex Smith before being tackled by cornerback Desmond King in the third quarter. On October 15, 2017, he earned his first career start after Albert Wilson suffered a knee injury and Chris Conley was placed on injured/reserve with a ruptured achilles. He made one reception for 16-yard in their 19–13 loss to the Pittsburgh Steelers. The following week, he made his second consecutive start and caught a season-high five passes for 69-yards in the Chiefs 31–30 loss at the Oakland Raiders. On December 31, 2017, Robinson made his eighth start of the season, replacing Tyreek Hill who was inactive after suffering a death in his family.