Basham is the son of long-time ARCA Menards Series driver Darrell Basham, and the older brother of Jason Basham, who competed in ARCA from 2003 to 2013.
Basham debuted in the ARCA Re/Max Series in 2001 at Gateway, driving the No. 34 Chevrolet for his father’s family-owned team, finishing 28th due to overheating issues. He made four more starts that year, with a best finish of 22nd at the DuQuoin State Fairgrounds dirt track. Over the following two years, Basham participated in three more races, driving for both his family’s team and Brad Smith’s team.
After a twelve-year absence from the series, Basham returned in 2015, driving three races for Darrell Basham Racing in the No. 34, achieving a best finish of fifteenth at the Illinois State Fairgrounds dirt track. He also ran select races in the Indiana Late Model Series that year, finishing tenth in points with a best finish of sixth at Movieland Speedpark. In 2016, Basham ran a majority of the ARCA schedule with the same family-owned team, in collaboration with Mullins Racing, finishing tenth in the points standings with a best finish of tenth at Springfield. He continued with the team in 2017, finishing thirteenth in the final points standings with a best finish of thirteenth at Winchester Speedway and Salem Speedway.
For 2018, Basham expanded his participation, running for Kimmel Racing at Pocono Raceway, finishing 28th due to overheating. He again finished thirteenth in the standings, with a best finish of eleventh at Elko Speedway. Prior to the 2019 season, Basham initially stated he had no plans to compete, but ultimately split time between Fast Track Racing, Kimmel Racing, and Darrell Basham Racing, finishing seventeenth in the standings after ten races, with a best finish of thirteenth at Lucas Oil Raceway and Salem.
In 2020, Basham returned to Fast Track Racing for a majority of the races, including a collaboration with Chad Bryant Racing at Kansas Speedway in the No. 77 Ford, where he finished twelfth, nine laps down. He achieved three top-ten finishes, including a sixth-place finish at Springfield, and finished eighth in the standings. He also ran three ARCA Menards Series East combination races, with a best finish of twelfth at Toledo Speedway. Basham returned to Fast Track for one race in 2021 at Berlin Raceway, finishing sixteenth due to handling issues.
In 2023, Basham returned to the series at Lucas Oil Indianapolis Raceway Park, driving the No. 69 Ford for Kimmel Racing, finishing 24th after eleven laps due to brake issues. He also competed at Bristol Motor Speedway, starting 28th and finishing 32nd after nine laps due to mechanical issues, and at Toledo, retiring after eleven laps and finishing seventeenth.
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