Ginn (1-1) picked up the win Thursday against Texas, allowing two runs on five hits and two walks across 5.1 innings. He struck out two.
Ginn (0-1) allowed three runs on seven hits and a walk while striking out five over five innings to take the loss Sunday versus the Tigers.
Ginn did not factor into the decision in Tuesday's win over the Mariners, allowing two runs on five hits and a walk while striking out seven over six innings.
Ginn is slated to start Tuesday's game against the Mariners in Oakland.
Ginn is scheduled to start Thursday's game against the Reds in Cincinnati, Jessica Kleinschmidt of the Oakland Athletics Radio Network reports.
The Athletics selected Ginn's contract from Triple-A Las Vegas on Tuesday.
Ginn (undisclosed) has given up eight earned runs on eight hits and two walks while striking out six over 7.2 innings in his two starts for Triple-A Las Vegas since being reinstated from the 7-day injured list June 2.