Born and raised in Brandon, Mississippi, Jonathan attended Jackson Preparatory School and Ole Miss, earning a degree in Business in December 2011. Jonathan began playing golf at the age of 4, and competitive junior golf at 10. He earned NCAA First Team All-American honors in June 2010, while also competing in top-tier amateur events nationwide. Jonathan launched his professional career in October 2011 by winning the PGA TOUR Q-School's Stage 1, held at Auburn, Alabama. He then closed out the year by missing the cut at Stage 2, held in Panama City.
After a slow start to his rookie year (2012), he gained momentum mid-year. He finished with three mini-tour wins (two NGA Tour and one Adams Tour), and was named the NGA Tour's Rookie of the Year, along with fellow rookie Ken Looper. In the fall, he was unable to advance past the second stage of PGA TOUR Q-School.
Jonathan's second pro golf year (2013) also started slow, with much attention given to game improvement. Once again he gained momentum mid-year, accumulating one NGA Tour win, and finishing 11th on the NGA Tour Money List. He was honored with the NGA Tour's Golf Achievement Award, given to the player who best exemplified a professional golfer both on and off the course. He capped off the year with a solid run through the Web.com Tour Q-School, finishing T32 in the Final Stage, and gaining Web.com Tour status for 2014.
2014 brought success on the Web.com Tour, including a 16th place finish on the Tour's money list. As one of "The 25", Jonathan was awarded status on the PGA Tour for the 2014-15 season.
Jonathan finished the 2015 PGA Tour season 179th on the FedEx Cup points list. Though guaranteed conditional status on the Web.com Tour for 2016, he elected to enter the Web.com Tour Q-School to improve his status. He successfully 'graduated', finishing T21 in the Final Stage, and solidifying his position on the Web.com Tour for 2016.
The 2016 Web.com Tour campaign was marked by significant game improvement and success on the course. Finishing 13th on the regular season money list, he again earned his PGA Tour card. Randolph made 17 of 20 cuts, with 9 top 25 finishes and 2-second place finishes. He led the Web.com Tour in rounds under par with 54.
During 2017, Randolph continued to show improvement, finishing his second year 160th on the FedEx Cup points list. A post-season 2nd place finish in the Boise Open of the Web.com Tour Finals earned him his PGA Tour card for his 3rd round on the Tour.