How can I get a Cantonese keyboard on an iPhone? Like Pinyin, but I need something that can recognize Cantonese instead of Mandarin. The only Chinese keyboards recognize Mandarin.
https://itunes.apple.com/us/app/canton-guang-dong-pin-yin/id385519764?mt=8 

or use stroke keyboard. 

Or ask Siri. The Cantonese version of Siri can understand Cantonese. 

Edit: Apple does not have such a keyboard and as you would know iOS does not allow custom keyboards. Anything suggested is a workaround. 
Apple now allows custom keyboards in iOS 8.

https://itunes.apple.com/us/app/cantonotes-jyutping-annotator/id354063453?mt=8
might also work for you.