The Smashing Pumpkins singer was impressed with the 14-year-old's hand painted version of his cover from the band's 2007 album 'Zeitgeist', and offered her free tickets to see them play.
After she tweeted the picture - which shows the statue of Liberty half submerged in water, painted in shades of red - he jokingly replied: ''@ParisJackson I'm glad you liked that cover! Not everyone likes that album haha (sic)''
He then tweeted: ''@ParisJackson I like you more and more! You'll have to come see us when we play. Not sure where you are but we'll hook you up for passes.''
Paris - who is the daughter of late pop singer Michael Jackson - replied: ''Best day ever.''
Meanwhile Billy is hoping to follow up his band's 'Oceania' album, released earlier this year, with another record soon which he has warned will be ''a cruel record.''
He told MTV: ''I'm starting to write new songs for the next Pumpkins album. I got a lot going on. I have a title for the next album but I won't tell. It's going to be a cruel record. Vengeance is mine.''