The 30-year-old will stay on loan with Doncaster until January.
Kirkland spent time with Leicester last season and has not featured for Premier League side Wigan since January.
The highly-rated goalkeeper could make his debut for Doncaster Rovers against Leeds United on Friday.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.