Can I patent the point system on my website?

That's extremely difficult to say. The United States Supreme Court in 2014 handed down a judgment in the case of Alice Corp. vs. CLS Bank that had the practical effect of making it very difficult to obtain a patent on software (and business methods). This is not to say that it would be impossible for you to obtain a patent in the United States. But before you expend a lot of money and effort on pursuing a patent, you should confer with a seasoned patent prosecution attorney who can advise you to what extent the Alice case might constitute a roadblock for you. If it is problematic, then you should definitely talk to your attorney about other means of protecting your intellectual property. If it is not problematic, then you should probably talk to your attorney about performing a prior art search so you can have a feel for the lay of the land with regard to existing technology before you go to the trouble of drafting a patent application.