Hard to picture without seeing it or at least a photo but you can always divert run-off around specific areas. Several methods available including trench or plain old 4" black perforated drainage pipe.

The bigger problem with a sloped garden is maintaining good soil moisture levels as the high dries and the downslop remains overly wet.

But chain link fencing isn't going to keep deer or rabbits or squirrels, etc. out anyway. They go right over-through-and under it. So if there is a better area outside the chain link that can be better fenced for varmints go for it.

Dave