After the suspension four years ago, Alfonzo said he never knowingly took steroids but did take medicine for bronchitis while home in Venezuela.
Manny Ramirez and Guillermo Mota are the only other major league players to be penalized twice for positive drug tests.
Baseball began testing with penalties in 2004. Under the current rules, a third violation would carry a lifetime ban.
Alfonzo is a .240 career hitter with 17 homers and 67 RBIs in 591 at-bats over 193 major league games. He has also played for San Diego and Seattle.
AP Sports Writer Ronald Blum contributed to this report.
Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.