Well, to be honest you can post poetry in *any* format. If you want to use a blogging software, or CMS, you certainly can. On the flip side, you could easily just code a website to include the poetry, and even format it visually if that's what you want to do with it.
There is no need for special 'software' just to post your writings. Heck, I've posted story snippets that I've been working on in my website with simple paragraph breaks. I believe in the minimalist approach: if I can do it without special software, I'll do it that way.
Of course, as always, your mileage will vary due to road conditions and speed. Or should I say 'due to choices and complexity'?