Hey Chuck,
I am assuming that you are talking about the wire that goes from the circuit board to the back of the antenna jack. If that's the case then the quick answer is yes, it is an easy fix. You do not need to use coax for this though. A piece of solid wire would be fine. The size (gauge) should be the same or larger. Keep it as short as possible. It does not need to be insulated either but can be. Look at a few CB repair videos on YT and look at how the wire is done if you need to. Lastly, I am also assuming that the antenna jack was loose and when you tightened your coax to it the jack spun and broke the wire. If that is the case make sure you fix that as well!!!! I know that some folks use locktite on those to help keep it from coming loose again. If I am mistaken in any of my assumptions just let us know so we can give you better counsel.