There's no hard and fast rule or a standard age really. I, myself, became a bookworm at the age of 4 and I started reading by myself at the age of 3. I reckon it has alot to do with the fact that I was always surrounded with books instead of toys. If you want to cultivate a reading habit at such a young age, perhaps you can do the same. Always have books around and read to your child whenever you can :)
Reading habit needs to be inculcated right from childhood. Given the right environment, kids as young as 2 yo might love flipping through picture books and picture story books. Once that sets in, kids start reading regular books at the age of 3.5-5 years.