Stinson is 4-4 with a 4.23 ERA in 15 starts for Norfolk, with 94 hits allowed, 34 walks and 58 strikeouts in 89 1/3 innings.
Stinson went seven innings on Saturday and would be working on short rest if used tonight.
Manager Buck Showalter prefers having a right-hander to back up a left-handed starter. Wei-Yin Chen comes off the disabled list to face the Rangers tonight in the second game of their series.
Also, Stinson is on the 40-man roster, so a corresponding move isn't necessary.
Two other 40-man candidates, Mike Belfiore and Tsuyoshi Wada, are left-handers and will remain with the Tides.
Stinson also is a hot hand, having gone seven innings in each of his last three starts. He's allowed six earned runs and 10 hits.
Stinson made one start with the Orioles on April 24 against Toronto, surrendering four home runs in 5 2/3 innings and being optioned back to Norfolk.
Gausman figures to join Norfolk's rotation after being removed from the Orioles bullpen following last night's 8-4 loss to the Rangers.