Deer can be hunted in Tomb Raider (2013) to gain XP. There are a lot of deer on the island. They appear at random in the forest.
When Lara first obtains the bow from the Dead Hunter in Woman versus Wild she sets out to hunt for the meat of a deer. This is the only time in the game Lara has to hunt to continue the story.
Deer may attack Lara when they feel threatened, but it is unlikely that they will hurt her enough to kill her.