Marine lost their sponsorship for the third round tie when an advertiser pulled out.
Carragher agreed to step in and sponsor the dugout and the warm-up tops through his JC23 Foundation.
"We are indebted to Jamie and the JC23 Foundation," chairman Paul Leary said in a statement.
"The JC23 Foundation do magnificent work in helping young people not just in Liverpool but right across the world. We are proud to partner with them on this special occasion."
Carragher's charity focuses on supporting sick, disabled and disadvantaged children and also provides services to community organisations and young people.
As the tie is behind closed doors, the club are also holding a raffle to try and raise funds.