Introversion's solid fan base is partly based on the fact that they are firm supporters of the Linux operating system. Their games are planned from the beginning to support most reasonable platforms and Prison Architect has already been made compatible to a variety of Linux operating systems such as Ubuntu and Debian.
As of the release of Alpha 10, an official Linux Build is available both via Steam and as a standalone download. While developed for Ubuntu, it also works under Debian, Linux Mint and Arch Linux. Due to the way Steam uses a standardized set of libraries that it guarantees to be available for games, it should run on any Linux version you can run the Steam client on, if your machine is otherwise up to spec, taking especially note of your graphics drivers.
Running Prison Architect with WINE
Prison Architect has been reported to run under WINE, however if you run Debian you may have to install the libwine-ldap package. More information and support can be found on the Discussion page.