Welding these rails is not as simple as that. These are pearlitic steel (0.7%C) and require thorough preheat.
and suitable filler metal as well.
As I see it, you've got basically three options:
1) as said above, splice with fish plates. These plates are designed to only touch the (bottom of the) rail head and the (top of the) bottom flange, so make sure you get the correct type.
2) most performed action is thermite welding. several contractors are licensed to do this on train rails, these guys are your best bet if you choose this option.
3) butt welding using cupper blocks as backing/molds, with either stick welding or cored wire process. Quality is lower than thermite welding but can be good enough for your situation (depending on ...)
Option 1) is the easiest, but the discontinuity will likely cause problems further down the road (shelling of the rail surface, sending vibrations into your structure, ...)
If you choose to continue with either 2) or 3), do not hesitate to continue in this thread as I've got quite some experience in railroad welding.
In the meanwhile, you should really check the exact grade of your rail (probably according to standard EN 13674 or the US equivalent) in order to know the hardness and chemical composition, as this will determine your filler metal (or thermite composition).