I saw this tweet yesterday.
Where did the now ubiquitous hamburger menu icon ≡ come from? Xerox—already in 1981 http://t.co/1fSOIYDvM4 by @geoffa pic.twitter.com/nWDI8E0ClX
— Antti Latva-Koivisto (@anttilk) 30 maart 2014
Although Xerox seems to be the first to use it on computer, there is no definite data (yet) on who used it on the phone first.
The icon is to be seen on the iPhone 3 back in June 2007 in some of their standard apps. That, to me, seems to be the first appearance on mobile phones, because other companies or apps that are named in the "first hamburger discussion" came later.
Like Google. Google is being named somewhere else on the interweb as potentially being the one who introduced the icon to mobile phones with Chrome. But Chrome's first beta was released in 2008 and the first Nexus phone was released in 2010.
But what for Android? That's Google too since they bought it. Their first phone was released in october 2008 however. Still later than Apple with the iPhone.