Wilkerson attended Midway High School in Waco, Texas. He enrolled at Cumberland University, where he played college baseball for the Cumberland Bulldogs. With Cumberland, he won a National Association of Intercollegiate Athletics World Series championship in 2010. Wilkerson posted a 14–1 win–loss record with 14 consecutive victories, 11 complete games, and a team-best 2.13 earned run average in innings pitched, while leading the nation with 125 strikeouts and being named both a Second Team All-American and the NAIA World Series All-Tournament Team. As a senior in 2011, Wilkerson set an NAIA record by pitching 54 consecutive scoreless innings streak from February 9 to April 8. He finished that season with a 12–0 undefeated mark and a 1.49 ERA, closing his college career by setting other NAIA record while winning 26 straight decisions. Besides, he earned First Team All-American honors and was named TranSouth Conference Pitcher of the Week three times. Doctors revealed that Wilkerson had pitched that season with a frayed ulnar collateral ligament in his right elbow. As a result, he underwent Tommy John surgery went undrafted out of Cumberland in 2011. He left baseball for two years while stocking frozen food shelves.
Wilkerson started his professional career in 2013 with the Fort Worth Cats in the independent United League Baseball. At the time, Wilkerson had to rebuild his mechanics completely with the help of his Fort Worth pitching coach and a private instructor introduced to him by his brother. He had a 9–1 record and a 2.74 ERA in 13 games.
He then was traded to the Florence Freedom of the Frontier League in the midseason, and finished the year with the Grand Prairie AirHogs of the American Association. Overall, he went 10–2 with a 2.96 ERA in 19 starts in the three leagues.
Boston Red Sox
In 2014, Wilkerson was 3–1 with a 3.35 ERA in 13 games for Grand Prairie, before joining the Red Sox organization when his contract was purchased from the AirHogs in August. After that, he went 5–1 with a 1.62 ERA in eight starts at short-season A-level Lowell Spinners. After that, Wilkerson posted a 7–2 record with a 2.96 ERA, 1.05 walks plus hits per inning pitched ratio and.218 batting average against in 17 outings for High-A Salem Red Sox in 2015. He then went 4–1 with a 2.66 ERA, 1.01 WHIP and.192 BAA in seven starts for Double-A Portland Sea Dogs. Wilkerson followed with a brief stint in the Arizona Fall League, as the starter sent to the Scottsdale Scorpions from the Red Sox, but he had to left the Scorpions to pitch for the USA squad in the inaugural World Baseball Softball Confederation Premier12 Tournament held in Taiwan and Japan in November 2015. In 2016, Wilkerson appeared in eight games for Portland, posting a 2–1 record with a 2.12 ERA and.175 BAA, striking out 48 batters while walking 14 in 44⅓ innings. He then gained a promotion to Triple-A Pawtucket Red Sox in late April. In 41 innings across eight Pawtucket appearances, Wilkerson went 4–1 with a 2.20 ERA, 1.07 WHIP,.222 BAA, 49 strikeouts, and 10 walks.
Milwaukee Brewers
On July 7, 2016, the Red Sox traded Wilkerson and Wendell Rijo to the Milwaukee Brewers for Aaron Hill. He spent the rest of the 2016 season with the Triple-A Colorado Springs Sky Sox. In 2017, he began the season with the Double-A Biloxi Shuckers. On September 15, 2017, Wilkerson was added to the Brewers' 40-man roster. On April 17, 2019 Wilkerson recorded his first MLB hit and homerun in the same at bat hitting a two run homerun off Michael Walka. On September 1, 2019, Wilkerson was designated for assignment.