Can the MagSafe charger be repaired

You sadly can't replace the cord. However, you can try to solder the wires in the cord back together and then put heat shrink over the damaged area in order to insulate it. Unfortunately, such a repair would be rather difficult considering that soldering can be quite tricky at times, along with the fact that soldering equipment can (most of the time) cost more than a replacement MagSafe charger. So your best option here is to simply get a replacement.