Bradley University

Bryan received a scholarship to play baseball at Bradley University where he was a 1st Team All-Missouri Valley Conference his sophomore and junior years recording 16 wins to 6 loses and an earned run average of 2.39 those 2 years. Rekar was later voted to the All-Centennial Missouri Valley Conference for Baseball and was elected into the Bradley University Hall of Fame for his baseball career.

Colorado Rockies

Selected in the second round of the 1993 amateur draft by the Rockies, he would wind up called up to the majors by them in 1995, pitching in 15 games. He would spend the next two seasons with the club compiling a 7-10 record with a 6.54 ERA.

Tampa Bay Devil Rays

In 1998, he wound up being drafted by the expansion team Tampa Bay Devil Rays. In 2000, he set a career high in wins (7), ERA (4.41), innings pitched (173.1) and starts (27).

2001 would not be his best season. He went 13 straight starts without recording a win. He finished that season with a 3-13 record and a 5.89 ERA in 25 starts. After that he was released from the team.

Kansas City Royals

In 2002, he signed a deal with the Kansas City Royals. Rekar only made 2 starts with the Royals, allowing 12 runs in those starts. After that, he was traded his former club the Rockies, for which he pitched on for the rest of that 2002 season.

Independent league

Rekar pitched for the Long Island Ducks for 2 years, compiling an 11–8 record.