Robert Doyle and his daughter Alex have raised $33,000 (£21,000) in an online campaign to fund the project, the Daily Express reports.
They intend to send the replica into space with a camera on the outside, allowing pictures of the Tardis in flight to be sent back to Earth.
Doyle, from Florida, said: "I was always a Doctor Who fan in school - I wore a Doctor Who scarf. Tom Baker was my favourite - he was always The Doctor to me.
"The bug caught on in an infectious way so we wanted to do something to celebrate the show we both enjoy so much.
"We mentioned putting a Tardis into space and our first thought was that it was a ridiculous idea. But at the same time it was definitely appealing so