New the polkadot js Api is fully compatible with React Native.
Reference:
polkadot-js/api#481
polkadot-js/api#526
$ git clone https://github.com/polkawallet-io/polkadot-api-reactNative-debugging.git
$ yarn install
Start your Substrate local Node.
$ react-native start
With another terminal:
$ react-native run-android
iOS For:
$ react-native run-ios
With another terminal:
$ react-native log-android // or ios
The effect :
Special thanks to : @polkadot{.js} & @jacogr