Arrington is the son of Buddy and Jeanette Arrington. He was a regular presence at his father's NASCAR events from childhood, and his interest in engine building was ignited by Maurice Petty, the engine builder at Petty Enterprises. Arrington developed his skills working at the Petty shop in Level Cross, North Carolina.
He made his first Winston Cup Series start in 1974 at age seventeen and competed in the series until 1980, making nine starts in total. His best result was a twelfth-place finish. After graduating high school in 1975, he took on the role of crew chief and engine builder for his father Buddy's racing programme, formalising what had been an informal involvement in the sport.
Arrington played a significant role in Dodge's re-entry into American stock car racing. He built engines and supplied parts for Dodge teams as the manufacturer returned to ARCA competition in 1991, followed by involvement in Trans-Am and the Craftsman Truck Series from 1995. This work positioned him as a key technical resource for Mopar-aligned teams during a formative period for Dodge's return to the sport.
In 2000 Arrington founded Arrington Manufacturing, Inc. in Martinsville, Virginia, operating simultaneously as Arrington Engines. The business built race engines for Dodge-affiliated Truck Series teams, including Bobby Hamilton Racing — of which Arrington was also a partner — and Ultra Motorsports. The company's work produced NASCAR Craftsman Truck Series championships in 2004 with Ted Musgrave and in 2005 with Bobby Hamilton, back-to-back titles that confirmed Arrington's engines as among the most competitive in the class.
When Dodge withdrew its support from the Truck Series in 2009, Arrington pivoted the business toward the aftermarket parts sector while simultaneously beginning to supply engines to the rookie Cup team Tommy Baldwin Racing, extending a working relationship that had begun in the NASCAR Nationwide Series.
In 2011 Arrington established Race Engines Plus (REP) in Concord, North Carolina, the hub of NASCAR's technical infrastructure, headquartered on Weddington Road. The new company built race engines for NASCAR, NHRA, and SCCA competitors, and also provided contract engine building services for private clients. In 2023 Race Engines Plus and its facilities were acquired by off-road and NASCAR competitor Robby Gordon, who rebranded the operation as Speed Engines.
Arrington's ties to Dodge persisted beyond his racing-engine work through the supply of customised HEMI engines for road-going vehicles.
His father Buddy Arrington, a long-tenured NASCAR independent driver, was inducted into the Mopar Hall of Fame in 2015. In 2012 Joey Arrington founded a new NASCAR Camping World Truck Series team, continuing the family's involvement in the sport at the team-ownership level.