I have seen both usages.
- Stay tuned on our Facebook page to know more
- Stay tuned to our Facebook page to know more
But don’t know which one is more appropriate. Please help me figure it out. Thanks
There is also "stay tuned in".
Each of these three is something of an anachronistic idiom, as the "tuned" used to refer literally to the tuning of the radio receiver. This carried forward easily when television came onto the scene, since TVs originally received broadcasts, like radios do. With cable TV, webpages, podcasts, and such, literal "tuning" is gone, and the choice of preposition becomes less clear.
I would say that "in" and "to" are more natural to use with "tune", but I would say that "on" is more fitting for something like Facebook. So I generally wouldn't ask people to "tune" to my Facebook page , but if I did, I would encourage them to "tune in" or "tune to".
 Instead, I would encourage them to "return", or "visit", or "subscribe", or "link", or "RSS" if the audience was geeky enough.
Objectively speaking, according to Google Books Ngram Viewer, stay tuned to our is the only phrase with any hits when looking at the printed word. (And this is comparing on, to, and in.)
Strangely, despite the results claim that it "yielded only one result," if you click stay tuned to our at the bottom of the results page, you'll find multiple instances of the phrase. But there certainly aren't any results when using the other prepositions.