Parton launched it in Rotherham in 2007 after pioneering the scheme in the US.
Chris McKay, head of Canterbury Children's Centre, said the project would help families who could not afford to buy books.
The centre would be the 31st place in the UK to start an Imagination Library.
Ms McKay said: "Books are expensive and if people are on limited income then there are difficult choices to be made and sometimes books can be seen as a luxury.
"This is a means of getting books into homes where they might not normally be able to access them."
Rotherham was the first place in the UK to adopt the scheme, which has now grown to operate in Wigan and a number of locations in Scotland.
Alison Lilburn, manager of the Imagination Library in Rotherham, said it had proved a success.
"We have looked at the early years foundation stage profiles and compared those children who are receiving the Imagination Library books to those who aren't.
"In the area of communication, language and literacy there has been a 5.2% difference in performance, which is really encouraging."