There's an infinite amount of ways that we can go about creating art as we all solve the same problems in different ways. So while it is impossible to have a completely original style (we are all influenced by what we come into contact with), it is possible to have your own tweaks and twists to it.
Honestly, I don't really see what the big deal is about having your own style. Usually when I hear about style from someone it's just an excuse to avoid having to fix anatomical or other problems. In the end, we're all trying to do the same thing which is to represent reality on paper (or a screen). I personally don't care about my style, I just want to create art that I and others can enjoy looking at.