He has paid for two coaches to visit the artefact in north Italian city, with the first group leaving next Wednesday.
Both groups will see the shroud before Pope Francis himself visits it, on June 21st.
Some believe the Turin Shroud, a linen cloth, covered Christ's body in the tomb.
The pontiff said in 2013 that he wanted "a poor Church, for the poor".
Since then, he has spearheaded several acts of kindness to the less fortunate.
In the last few months, homeless people were reserved VIP front-row seats at a charity concert on Vatican grounds, and given a tour of the Sistine Chapel and Holy See gardens.
And St Peter's Square has installed hot showers for rough sleepers to use, gathered volunteers to give free haircuts on certain days of the week, and sleeping bags with the Vatican crest.
Some have complained about Pope Francis's gestures, saying it's causing businesses to lose money, and that waste products and sharp objects are being left there.