Ok, this is an intransitive verb.
It means to curve body and draw up legs: to sit or lie with the body curved and the legs tucked up.

It also means, to feel extremely embarrassed: to be overcome with embarrassment, revulsion, or some other strong feeling (informal).

I took this definition from Microsoft® Encarta® Encyclopedia 2009.
1st meaning.- curl up in bed with a good novel.
2nd meaning.- When I realized my mistake I just wanted to curl up and disappear.
Another example, "to curl up with a good book"
by Froc March 09, 2010

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