This answer states that the minimum rep is 2000, but you have to search around to find this. I suggest listing it in the FAQ page.
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Done quite a while ago: http://meta.stackoverflow.com/privileges/suggest-tag-synonyms
While not the solution you were looking for, this is included on the synonyms page:
Since this is on exactly the page in which it matters, you'd have to search even less than if it was only in the FAQ. The FAQ deals with the site in a very broad way, and I don't see the need to introduce all users (especially new users) to this detail. However, mentioning something about synonyms in the FAQ (even just a link to an announcement or otherwise) would be useful.
(I don't know if this was shown on the synonyms page when you posted this question, or if it was later updated.)