Pappas was selected as a catcher by the California Angels in the 1984 amateur draft, but made his major league debut with his hometown Chicago Cubs in 1991. Pappas only played in 7 games for the Cubs who released him after the season. He signed with the Kansas City Royals, who later traded him to the Chicago White Sox.
In 2004, he represented Greece at the 2004 Athens Olympic Games. Currently Pappas is a coach at Cangelosi Baseball.