Depends on what it's used for... and how it's damaged. If this is something that simply has a gash down the length of it and you need to slide a bearing over it... I'd just grind it smooth with a flap disc and slide the bearing on provided it will fit tight. On the other hand... if the bearing has turned on the shaft and worn the radius down you would be better off making a new shaft or at least building this one up and turning it properly. I've built up and ground down with flap discs for fitting sprockets and that type of thing... but to fit a bearnig you need a concentric surface. If you don't have that the bearing will point load and crack the inner race because it's not properly supported... Again... that's a factor of the load applied and the size of the bearing. Sometimes you get away with it but in my experience that's not very often.
Another cheap/nasty trick to get moving, if need be... wrap the shaft in shim stock and fill with green Loctite (Sleeve and Bsaring retaining compound)... That will take up some slack and set it so it works for a while.