"Nature's calling" or "Nature calls", is slang for "Excuse me, I have to pee." You might hear someone say this to a friend (at a bar, for example) after having several drinks. It is very informal language said among friends.

Nature is calling me. Without the article, it's incorrect with it. A variation is 'I have to answer the call of nature.' Anyway, it's a way for a person to say they need to go to the toilet without explicitly saying that. Some people feel a little uncomfortable speaking so directly about this subject.

When you say, "Nature is calling," it means that you need to use the bathroom. People use it in a humorous way. It is not the most polite way to say it.