Goalkeeper Randolph is named in Martin O'Neill's provisional 29-man squad for their forthcoming friendly game against Serbia.
The squad will be shortened ahead of March 2, to facilitate injuries etc.
The Republic host Serbia at the Aviva Stadium in Dublin on March 5.
To date Randolph has two senior caps for his country.
Meanwhile, midfielder Callum Reilly is named in the Republic's U21 squad for their Euro 2015 U21 qualifier against Montenegro.
The fixture will be played on the same night as the senior side but at the Tallaght Stadium in Dublin.
Twenty-year-old Reilly has made eight appearances for the U21s so far.