The offer is available by calling the RFL Ticket Office on 0844 856 1113, between 9.00am - 5.00pm.
England coach Steve McNamara said: "The Origin game does form an important part of our preparations for the World Cup but more importantly it's a fixture we very much want to win.
"We spoke at length about playing the Exiles during our recent camp at Loughborough and it was clear from all the players that there is a real hunger not just to feature in this match, but to win it.
"It's a one-off game and an opportunity for all of us to put down a marker.
"The players are hoping to have the whole country behind them this year: they got a huge lift from the amazing support we got in the 2012 Four Nations final against Australia and it would be fantastic to have that passion roaring us on against the Exiles."
Tickets for the International Origin Match at The Halliwell Jones Stadium, Warrington, on Friday June 14 cost from £20 (£15 for 65+ and students, £10 for under-16s) and can be purchased by visiting www.rugbyleaguetickets.co.uk
To take advantage of the free shirt offer fans should call the RFL Ticket Office on 0844 856 1113 between 9.00am - 5.00pm. The offer will end at 5.00pm on Friday or when stocks run out.