Marcus Georges-Hunt had 12 points on 4 of 5 shooting from beyond the arc in the first half for the Yellow Jackets (8-2), who won their fourth straight and improved to 6-0 at home.
Matt Groselle and Lawrence Miller each had nine points for The Citadel (3-7), which shot 25.4 percent from the floor for the game. Stephen Elmore finished with eight points and 10 rebounds.
Carter had nine points and Julian Royal added eight for Georgia Tech, which shot 43.7 percent.
Kentucky transfer Stacey Poole, who became eligible after the first semester, made his debut for Georgia Tech and scored all of his seven points in the second half. He also had five rebounds.
The Yellow Jackets' biggest lead was 36 points with 6:19 to play.
Georgia Tech made of nine of its first 13 shots and led 20-3 before the game was nine minutes old as the Bulldogs started 1-for-10. The Citadel got within 22-10, but Georgia Tech then went on a 17-0 run and the lead was 41-16 at halftime.
The Citadel shot just 19.4 percent in the first half and was 1-for-11 from behind the 3-point arc at intermission and 3-for-22 for the game. Van Scyoc missed eight 3-point attempts.
Ten players scored for the Yellow Jackets.
Georgia Tech played its second straight game without Jason Morris, who is battling plantar fasciitis. The junior wing, a key reserve, is averaging 4.9 points per game.
The Yellow Jackets have home games against Fordham next Saturday and UT-Chattanooga on Jan. 2 before opening ACC play by hosting Miami on Jan. 5.
Georgia Tech's losses are to California in the DirecTV Classic at Anaheim, Calif., and at No. 10 Illinois.