Unfortunately no, connecting your Xbox (I take it a 360) to the internets takes a different type of cable, an UTP or LAN cable, and a bit of effort.
Telephone cables usually have 4 small copper connectors on each end while UTP cables have 8 (some old ones have 4 or 6 though). The connectors are also wider.
You'll have to connect your Xbox to a modem/router to be able to go online with it. There should be a detailed explanation on how to do that in the booklets that came with the Xbox.
Or, if you have a pc with a working internet connection and 2 LAN-ports you can channel your internets through your pc to your Xbox. Just don't go Youtubing while gaming online.
Hope this helps.