A 3-star recruit, Sprinkle accepted a football scholarship from the University of Arkansas over offers from Kansas, Louisville, Mississippi State, and Purdue, among others.

[3][4][5] As a redshirt freshman in 2013, fellow classmate Hunter Henry received most of the targets at the tight end position.

[7] As a junior in 2015, even though Henry recorded a majority of the production as the starter, Sprinkle had 27 receptions for 389 yards and led all Southeastern Conference tight ends with six receiving touchdowns.

On November 28, 2016, it was announced that Sprinkle had accepted his invitation to play in the 2017 Senior Bowl, along with Arkansas' punter Toby Baker.

[11] Sprinkle was one of 19 tight ends who received an invitation to participate at the NFL Scouting Combine in Indianapolis, Indiana.

[13] On March 15, 2017, Sprinkle opted to participate at Arkansas' pro day, along with Cody Hollister, Dan Skipper, Jeremiah Ledbetter, and 13 other prospects.

At the conclusion of the pre-draft process, Sprinkle was projected to be a fourth or fifth round pick by NFL draft experts and scouts.

[22] Head coach Jay Gruden named him the fourth tight end on the depth chart to start the regular season, behind veterans Jordan Reed, Vernon Davis, and Niles Paul.

[23] He made his professional regular season debut and first career start during a Week 3 matchup against the Oakland Raiders after being inactive for the first two games.

On November 19, 2017, Sprinkle caught his first career reception on a seven-yard touchdown pass from quarterback Kirk Cousins during Washington's 34-31 loss at the New Orleans Saints.

[31] On April 7, 2021, Sprinkle signed as a free agent with the Dallas Cowboys, with the intention of being used as a blocking tight end.

[39] On December 27, 2016, Sprinkle was involved in a shoplifting incident during a Belk Bowl sponsored event in Charlotte, North Carolina.