One of the two debutant teams this season, the Supergiants have already lost four of their star international players -- Australian duo of Steve Smith and Mitchell Marsh, South African Faf du Plessis and Englishman Kevin Pietersen -- due to injury.
Earlier, another Australian batsman Usman Khawaja was also called in to join the IPL franchise for the rest of the tournament.
"We lost four crucial players, but we are looking ahead," RPS chief executive Raghu Iyer said.
"It is a challenging time. Before we could settle down we lost the core group of players around whom you build a team," he added.
Bailey, who was the captain of Kings XI Punjab in the previous season, was overlooked during the IPL auction in February.
Bailey had earlier also been a part of the now defunct Chennai Super Kings team.