Orbach was born in Petah Tikva, Israel. He attended a Hesder yeshiva, serving as a staff sergeant in armour corp. He later worked as a journalist, producing columns for Yedioth Ahronoth and serving as a co-host for the Army Radio mid-morning show 'The Last Word'. He has written several children's books, including Donkeys on the Roof and Other Stories, and a dictionary of Religious Zionist slang, My Grandfather Was a Rabbi. He founded and edited the popular Israeli children's magazines Otiot and Sukariot.
Prior to the 2009 elections, he joined the Jewish Home. Following a split in the party, in which several members left to re-establish the National Union party, he was placed third on the party's list, and entered the Knesset as it won three seats. For the 2013 elections he was placed sixth on the Jewish Home list, retaining his seat as the party won 12 seats. He was appointed Minister of Pensioner Affairs on 18 March 2013.
Orbach currently lives in Modi'in with his wife and four children.