This looks at first sight like a mistaken attempt at a literal translation, but I think it might be a way of capturing the idea without sounding too modern. As in the original, "hair" is used to express the very slightest, most minimal contact. It can be extended to "a hair of the head of", but I think you can omit "the head of" if you like. An emphatic variant might be "so much as a hair of".

A modern near-equivalent might be "never laid a finger on". She's been accused of attacking the Jesuits and is denying it.

Here's an example from 1801 applies to a non-human object:

"He congratulated the House on the vigilance of Ministers, who, whilst they acted upon emergencies with vigour, did not touch a hair of the head of the Constitution."
https://books.google.es/books?id=JVUxAAAAIAAJ&pg=PA186&lpg=P...

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Note added at 9 hrs (2015-10-06 08:27:07 GMT)
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"Un pelo de la ropa" is an idiomatic set phrase, and it already was in the period Sor Juana was writing. Here is the definition from the first RAE dictionary of 1737:

"No tocar al pelo de la ropa. Phrase con que se dá à entender, que no se ha ofendido ni hecho daño à alguien, ni dicho cosa sensible."

So I think it is appropriate to use an idiomatic set phrase to translate it, and the one I've proposed seems to me to fit the bill.

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Note added at 10 hrs (2015-10-06 08:32:32 GMT)
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So what she means is "I have done absolutely nothing to offend the Holy Company" (i.e. the Jesuits).

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Note added at 1 day9 hrs (2015-10-07 08:00:26 GMT) Post-grading
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Hi Erik,
Thanks! I have a facsimile copy of the first DRAE, not an original! I bought it some time ago because I used to do a lot of historical research, and it's really invaluable for early modern texts. But nowadays you can consult it online, along with many other early dictionaries, via the RAE's excellent NTLLE site:
http://ntlle.rae.es/ntlle/SrvltGUILoginNtlle
Just click on the first icon top left, enter your search term, and youl get a list down the left-hand side of the screen of all the dictionaries in the database in which the term appears. You click on the one you want to see and you can view a facsimile of the dictionary entry. Very, very useful if you're dealing with historical usage!