Rice, 18, only made his West Ham debut as a late substitute in the Premier League against Burnley on Sunday.
In March, Rice was named the Republic's Under-17 player of the year.
Rice, who can play in defence or midfield, is the second call-up to the squad in 24 hours after Preston's Alan Browne was drafted in on Monday.
The Republic face Mexico in New Jersey on 1 June and take on Uruguay in Dublin three days later before the qualifier at home to Austria on 11 June.
Uncapped Corkman Browne previously played for the Republic's Under-21s.
The 22-year-old joins his Preston club-mates Aiden McGeady, Daryl Horgan and Andy Boyle in Martin O'Neill's squad.
Browne joined Preston from Cork City in 2014 and made 35 appearances for the Championship club this season.
The Republic are level on points with leaders Serbia after five series of games in their World Cup qualifying group.
Wales and Austria are both four points off the pace.
West Ham youngster Declan Rice has been called up by the Republic of Ireland for their upcoming friendlies and the World Cup qualifier against Austria.