The iOS version of the runtime SDK doesn't support shapefiles at this time. This is supposed to be supported in the next version.
Thanks, Michael! Is there any way to read them? May be converting them to another format or adding all files into one gdb file?
You can add them to a file geodatabase and then export them to a runtime geodatabase in ArcGIS using the "Create Runtime Content" tool. This will create a read-only database and you can load the feature layers up in the mapView of your app.