I was trying to install a new ceiling light fixture in our bedroom. When drilling a new hole to run the romex down to the light switch I nicked an existing wire. Can this be repaired or will the wire need to be replaced entirely?

The red insulation on that wire is damaged and if pulled back the copper wire is visible as seen in the link.

http://www.flickr.com/photos/93135998@N03/

Any help is greatly appreciated. Currently has electrical tape around red wire and around black wire on damaged places, and finally wrapped around the whole wire. I have power to this shut off at the breaker.

I wouldn't take the chance... replace the wire.

Where is that cable located in the house? Is there any slack in the cable?

If located in attic and you have enough slack, you can cut the wire and install it into a junction box. The box can not be covered in the wall or ceiling. Must be exposed and accessible.

Chuck