Kori was born in Chilauli, tehsil Derapur district, Kanpur, in a korifamily which is enlisted in the Scheduled caste list in Uttar Pradesh. His father's name was Ghaseete Lal. He passed high school from R P S Inter CollegeRura, Kanpur. After leaving school, he became a follower of freedom fighter Shambhu Dayal Chaturvedi of village Badagaon Bhikkhi tehsil Derapur, district Kanpur. He stayed with Shambhu Dayal Chaturvedi as a family member until Chaturvedi's death. Shambhu Dayal Chaturvedi was a political guru to Radhey Shyam Kori.
Politics
In Congress
His first step was from village politics. He officiated as Pradhn of Badagaon Bhikkhi of tehsil Derapur for about 20 years and also officiated as Block Pramukh of Derapur district, Kanpur. Shambhu Dayal Chaturvedi was a very active worker and leader of the Indian National Congress, so Kori also joined the Indian National Congress with the help of Chaturvedi. After some time he became General Secretary of the INC party of Kanpur district.
In 2004 he joined Samajwadi Party and fought election to Parliament as the MP from Ghatampur Constituency and became the winner from this seat. He defeated Pyare Lal Sankhwar of BSP.