No, you can’t get cancer from a tablet. Some chemicals (like cigarette smoke) increase the chances of getting mutations in cells, and therefore increase the risk of getting cancer. So I suppose that if you made tablets containing dangerous chemicals like that, those tablets would increase your risk of getting cancer if you took them. But there would be absolutely no good reason to do that!
There are some tablets that are used as medicines that can make you more likely to get cancer – like the hormone replacement therapy that some women take when they are going through the menopause. These medicines are only legal because they have benefits for some people that are good enough to outweigh the extra cancer risk.