This is another great day for the React Native community, Naoufal Kadhom is not done yet releasing components.
Warm your fingers.
Touch ID? Got you covered.

react-native-touch-id on GitHub

react-native-touch-id is a React Native library for authenticating users with Touch ID.

var TouchID = require('react-native-touch-id');

var YourComponent = React.createClass({
  _pressHandler() {
    TouchID.authenticate(function(error, success) {
      if (error) {
        // Failure code
      } else {
        // Success code
      }
    });
  },

  render() {
    return (
      <View>
        ...
        <TouchableHighlight
          onPress={this._pressHandler}
        />
          <Text>
            Authenticate with Touch ID
          </Text>
        </TouchableHighlight>
      </View>
    );
  }
});