I just started learning japnese, and I finished hirigana a couple days ago. So i'll say maybe 2-4 weeks. (It really depends how much time you spend tho.)
It depends on what you use and how much time you spend practicing. If you truly want to master hiragana, eventually you have to start reading things in it regularly, like sentences and words on renshuu.
Like everyone else has said, it depends on how often you study and read hiragana. You can definitely learn a lot faster if you pick up some word schedules and spend some time reading hiragana outside of your studies. Personally, I bookmark a bunch of wikis in Japanese and play Japanese video games every now and then. You don't have to understand every word you see, just focus on reading the kana one-by-one until you can recognize all of them.
I'm in a position to hear a lot about how other people do in renshuu, and I've heard from 3 days to a couple of months. The short answer is - it all depends on your study habits, life situation, and a bunch of other things. No need to worry comparing yourself to how long it takes anyone else :)
I learned both hiragana and katakana in about a month with a 97% accuracy using the book “kana from zero.” Highly recommend these books. I combined book learning with free “kana” app from iOS store. It was before I found this one. The book teaches you roughly 10 kana per lesson. The app quizzes you on items you miss more often. It quizzes you on visual recognition, voice recognition and writing the letters in correct stroke order.
If you really buckle down and put effort towards studying every single day, it shouldn't take more than a couple of weeks. It depends entirely on your personal studying schedule, though.
