Ireland did not qualify for this summer's European Championships, but have friendlies against Andorra and Hungary this month.
Millers winger Ogbene has been included in the 27-man squad.
Ogbene was born in Nigeria but his family moved to Ireland in 2005 and he began his career with Cork City and Limerick. He declared for his adopted country last summer.
Ogbene joined Rotherham in 2019, but has had an injury not helped by injury, or manager Paul Warne's tendency at times to prefer wing-backs over specialist wingers such as the 24-year-old.
Sheffield United central defender John Egan and wing-back Enda Stevens are also in the squad.
The two away games will be played on June 6 (Andorra) and 8th.
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