There is a wide range of ARM devices that are capable of running a Plex media server. Unfortunately, Plex does not provide a generic package for ARM platforms but only installers for specific devices. Luckily, Jan Friedrich provides such a package.
You can install the server in four easy steps
wget -O - https://dev2day.de/pms/dev2day-pms.gpg.key | apt-key add - echo "deb https://dev2day.de/pms/ jessie main" >> /etc/apt/sources.list.d/plex.list apt-get update apt-get install plexmediaserver-installer
The remaining configuration works as usual. If you are missing the images (covers, fanart, and so on), you have to adjust the local authentication settings to allow access from your local network.