Usually this is done using a table view, which is basically a list of items as well, only with a checkmark instead of a radio button. Sometimes such lists are on a new 'page' in the navigation structure. How this fits in your navigational structure depends on the context.
There’s plenty of other alternatives that could be good, it really depends on the app’s structure. You’ll notice that lots of the options in Settings use a master/detail pattern for things that are effectively radio buttons. It’s a good way to go, especially with limited screen space.
Check out this easy seven step tutorial - iPhone UIButton tutorial: Radio Buttons by Mobisoft. It is what I have used for the past couple of years. There is too much code to replicate here, so beware of link death in the future. The steps are below:
Create a window based application in Xcode and name it “MIRadioButtonGroup”.
Create new “MIRadioButtonGroup.h” and “MIRadioButtonGroup.m” files
which extend from UIView. (Classes >> Add >> New File >> Objective C
Class. Select UIView in the “subclass of” list.)
Create a new group in the Classes folder and name it
“MIRadioButtonGroup”. Drag the “MIRadioButtonGroup .h” and
“MIRadioButtonGroup .m” files into the group.Now, add the images
“radio-on.png” and “radio-off.png” to the group.
Open the “MIRadioButtonGroup.h” file and make the changes in it, as suggested on the site.
Open the “MIRadioButtonGroup.m” file and put the respective code in it.
Now that we have created the “MIRadioButtonGroup” files, put the following code in the “MIRadioButtonGroupAppDelegate.m” file so that we can test them.
Save, build and run the project. The output will be Output1. Now uncomment the commented lines one by one and observe the output. It will be Output 2, Output 3 and Output 1 respectively.