Fast bowler Siraj, who has played 45 Tests, 50 ODIs and 16 T20Is, was named as a replacement after Rana was ruled out with an injury to his right knee that was sustained during the warm-up game against South Africa on 4 February.
The replacement of a player requires the approval of the Event Technical Committee (ETC) before the player can be officially added to the squad.
India will take on the USA in their first group stage match on Saturday. The match will begin at 7 pm.