Yes, there is a version of Tor Browser available specifically for Android. Installing Tor Browser for Android is all you need to run Tor on your Android device.
The Guardian Project provides the app Orbot which can be used to route other apps on your Android device over the Tor network, however only Tor Browser for Android is needed to browse the web with Tor.
The Guardian Project maintains Orbot (and other privacy applications) on Android. More info can be found on the Guardian Project's website.
We recommend an iOS app called Onion Browser, which is open source, uses Tor routing, and is developed by someone who works closely with the Tor Project.
However, Apple requires browsers on iOS to use something called Webkit, which prevents Onion Browser from having the same privacy protections as Tor Browser.
Learn more about Onion Browser.
Download Onion Browser from the App Store.
There is currently no supported method for running Tor on Windows Phone.
While both Tor Browser for Android and Orbot are great, they serve different purposes.
Tor Browser for Android is like the desktop Tor Browser, but on your mobile device. It is a one stop browser that uses the Tor network and tries to be as anonymous as possible.
Orbot on the other hand is a proxy that will enable you to send the data from your other applications (E-Mail clients, instant messaging apps, etc.) through the tor network; a version of Orbot is also inside of the Tor Browser for Android, and is what enables it to connect to the Tor network.
That version, however, does not enable you to send other apps outside of the Tor Browser for Android through it.
Depending on how you want to use the tor network, either one or both of these could be a great option.