I was wondering whether the deer would be able to smell bug repellent if you are wearing some while out hunting. Is there a specific type of bug repellent that can be used that is less likely to make deer shy away from the area?
Yes, deer will smell your bug spray. Even if you use all the fancy scent-eliminating sprays, soaps, and clothing detergents they can still smell you if you are sweaty. Most important is the wind factor: Deer will smell you if they are downwind of you.
NRA hunting advice for first-time deer hunters: http://www.nrainsights.org/Five_Things_fs.php.
I would say use the bug spray you would have used anyway. Just make sure you carefully monitor the wind and plan your hunting spot carefully.
During turkey season I practically bathe in regular deet based spray since turkeys can't smell. Thing is, this spring I had a deer walking around calmly 10-15 yards from me more than once. Can they smell it? Sure. Does it alarm them? Why should it? I would think only if they've made an association between it and danger.