If I define acronyms in the abstract, should I define them again in the rest of the paper?

Abstracts are read separately from the paper itself. They aren't an introduction, but more of a condensed version.

So if the paper defines an acronym, it shouldn't rely on the abstract for it. On the other hand, the abstract is supposed to be fairly short, so there isn't usually much of a case for defining acronyms there.

It depends on the paper, of course, but consider spelling out the whole term in the abstract if it is referenced only once there.

I was wondering if there is a rule regarding the above?

There is a simple rule: always do what is most helpful for your reader. Often your reader will not read the abstract of the paper at the same time as the body, so it would not be unusual for a reader to start reading the paper without first reading the abstract (perhaps having read it at some previous time). If they read from the start of the body, and are presented with acronyms that are not defined, that might lead them to a situation where they don't understand some part of your paper. I would therefore recommend erring on the side of caution and defining your acronyms in the body of the paper.

I would repeat it. Some people read abstracts only (e.g. Chem Abstracts is a pulication of abstracts). Those who are reading the paper may not read the abstract.

Really, each should be self-supporting. Otherwise, you start to morph the abstract from an abstract to an introduction.