What food is best for encouraging deer?
Judging by the way they attack grain hoppers put out for pheasants, roe must like wheat and benefit from it.
However, too much might induce bloating, while open-trough feeding would attract birds. If carrots and turnips are grown commercially in your area, they would also be of benefit.
A vegetable packing plant will have rejects available. The main thing is to feed a small amount at a time and to start early so the deer become used to what you give them.
A rapid change of diet, especially when they are already hungry, can lead to deer gorging on food they cannot actually digest because the bacteria in the rumen need to adapt to any change of diet and this may take a couple of weeks.
Feed regularly, otherwise a heap of food that could be used elsewhere will rot.
In the long run, planting browse, such as willow, will provide a good source of food all year round, provided you keep it well pruned.