Thanks to Jed Tiotuico that's taking advantage of the impressive PPSSignatureView for iOS and android-signaturepad for Android you can now start capturing signatures in your React Native apps.

react-native-signature-capture on GitHub

React Native library for capturing signature

User would sign on the app and when you press the save button it returns the base64 encoded png

var React = require('react-native');  
var SignatureCapture = require('react-native-signature-capture');  
var {  
  AppRegistry,
} = React;

var NPMTest = React.createClass({  
  _onSaveEvent: function(result) {
    //result.encoded - for the base64 encoded png
    //result.pathName - for the file path name
    console.log(result);
  },

  render: function() {
    return (
        <SignatureCapture
          rotateClockwise={true}
          square={true}
          onSaveEvent={this._onSaveEvent}/>
    );
  }
});