"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.
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)
