@Loh Jane,
You can say took, but there is no need to use "of a". Nobody I know ever says or writes it this way.
"A half hour siesta" is perfectly acceptable.
I took a half hour siesta.
I had a half hour siesta.
Although, if it is for only half an hour, I wouldn't go so far as to call it a siesta. More like a catnap, really.