"We made the decision to add Marcus to give us flexibility to play an all-rounder in the event the conditions require an extra bowling option in the lineup," national selector Trevor Hohns said in a statement.
Stoinis has played 24 one-day internationals and 17 Twenty20 internationals for Australia, but is yet to make his test debut.
The 29-year-old has scored 298 runs, including three half-centuries, and claimed 10 wickets in four Sheffield Shield matches in the 2018-19 season for Western Australia.
"Marcus has been a consistent performer this season, he's displayed strong all-round form in first class cricket and continued that form into the Australian ODI series against India," Hohns added.
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Meanwhile, Renshaw, who missed the first test, will link up with his Brisbane Heat team mates for their upcoming Big Bash League fixtures.
The second test begins on Feb. 2 at Manuka Oval in Canberra.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
