The award, for defensive excellence, will be officially announced in mid-November. League managers and coaches vote on the award but cannot list their team's players.
Late in the season, Rodriguez said he hoped to win the award again, but acknowledged: "I haven't had a good year; I have to be better."
Manager Kevin Kennedy and pitching coach Claude Osteen at times were unhappy with the way Rodriguez ran a game.
In another development, designated hitter Julio Franco filed for free agency. Chuck Berry, Franco's agent, described the move as a paperwork formality.
"We're still hopeful of working something out with the Rangers," Berry said. "But filing is Julio's right, and it gives him a chance to determine what interest there is out there."
Rodriguez, who turns 22 Nov. 30, is the second-youngest two-time winner in the history of the Gold Glove awards, which began in 1957. Hall of Fame catcher Johnny Bench was one month younger when he won his second consecutive award in 1969.
Rodriguez is the first AL catcher to win the award in two consecutive years since Bob Boone in 1988-89. With two Gold Gloves, Rodriguez is tied for eighth on the all-time AL list with Ray Fosse and Elston Howard.
Former Ranger Jim Sundberg leads AL catchers with six Gold Gloves. Bench is the all-time leader at the position with 10.
A year ago, Rodriguez threw out 51 of 104 runners for the AL's best rate (49 percent) among catchers with 70 tries. This year, Rodriguez dropped to fourth, throwing out 40 of 104 runners (38.5 percent). He was second in passed balls with 14.