Former Australian captain Smith, on the other hand, led the Royals to three victories in the five matches that he was captain, with one of the those games ending without a result.
Smith has left the group to join Australia's World Cup preparation camp and Royals head of cricket Zubin Bharucha believes Rahane can be the "guiding force" of the team as they hope to qualify for the IPL playoffs.
"We have requested Ajinkya to take on the captaincy of the team," Bharucha said in a statement.
"As a true Royal he has shown great courage and character in graciously accepting the responsibility, which accompanies this role, whilst it would have been easier for him to take a back seat and focus solely on his batting.
"He has consistently been part of the leadership team taking key decisions and we have full trust in him taking us to victory tomorrow."
Rajasthan, who are fifth in the table with 11 points from 13 games, must beat Delhi Capitals on Saturday to stand any chance of qualifying for the playoffs.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
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