Godfrey is making his third stint with the A's this season. He's 1-2 with a 4.71 ERA in four starts. He went 14-3 with a 2.68 ERA in 19 games, 18 starts, for the River Cats. He led the PCL in wins.
Carter was with the A's from June 23 to July 14 this year, appearing in 10 games. At Sacramento, he hit .274 with 18 home runs and 72 RBIs in 75 games.
"History suggests he takes awhile to acclimate," A's manager Bob Melvin said. "The numbers he's putting up recently suggest he's pretty comfortable."
Carter batted .133 (4-for-30) with the A's earlier this year.