There are two sides to this technical and legal.
On the technical side the main question is how portable does it need to be? If a system mounted in the back of a SUV or pickup is acceptable then it's certainly doable. Man-portable may be tricker.
You would need a mobile base station and something to power it. If you want to talk to the outside world you would need some kind of uplink (sattelite or possiblly short range microwave). If you want to receive incoming calls on your regular phone number then you would need a roaming agreement with your regular phone provider.
The hardware to run a base station is available off the shelf. See for example http://www.rangenetworks.com/products/ . The software is available as open source.
Then there is the legal side. Mobile phones operate on specific channels within specific bands. To operate legally is likely to require specific authorisation from your country's radio regulator and/or an existing cellular operator.
There is some overlap between the 900 MHz US ham band and the cellular bands used in europe but I don't know if this overlap is sufficient to allow running a functional network. http://n9xlc.blogspot.co.uk/2010/10/ham-radio-cellphone-network.html