The command below replaces the player's held item slot with a carrot if it has anything other than a carrot.

/item replace entity @a[nbt=!{SelectedItem:{id:"minecraft:carrot"}}] weapon.mainhand with minecraft:carrot 

If this command is put in a repeating command block and you eat a carrot in survival mode it will try replace the item in your hand, but it will appear invisible until you update the slot.

http://youtu.be/WQz-VN4vXoM