something like this would probably work.
personally I'd prefer a switch, as the other port could be used in future for something else, but a splitter like that would work too.
note that as it says on there, they're used in pairs because:
Cat5e only utilises 2 of the four pairs of wires (wires 1,2,3,6) inside the cable. These splitters allow data from one connection to be sent down the usual wires 1,2,3,6 and the data from the second connection to be sent down the other cables (wires 4,5,7,8).
so you'll need one of them plugged into two ports on your router, and the other into your PC and xbox.
.. hopefully your network is not gigabit.