I have limited knowledge about this, so I’m not 100% sure but; I believe that the Rust server files and application is not currently made public. Only approved companies may host Rust servers, and they must follow a ToS that ensures they do not release server files/applications or give too much access to files/folders. There are copies of the server files you can get to my knowledge, but they must be enabled with a password or they won’t start up.
Basically, at this time, there is no (legal/easy) way of acquiring the server application and hosting it yourself. To get a server you must buy/rent it from a FacePunch approved server company, as they are the only ones with the ability to host this game.
Quite unfortunate, honestly. I’m not sure of the reasoning behind this approved hosts only shit, but I was in the same boat as you were. Information is scarce on this subject. I eventually gave in and bought a server from FPSplayers, after realizing my attempt to get it going on my CentOS server was futile. FPSplayers is good, as far as hosts go, but I can’t stand not having the control and root access to do proper backups, configuration, control, etc. Hopefully they will publicly release the server application when it is out of Alpha.