Is it possible to use Polymer inside of React?

Yes, it is possible.

1. Create a polymer element.

   <link rel="import" href="https://stackoverflow.com/questions/26365545/bower_components/polymer/polymer.html">
   

   Polymer({
       is: 'calender-element',
       ready: function(){
           this.textContent = "I am a calender";
       }
   });
   

2. Make the polymer component a html tag by importing it in a html page. E.g. import it in the index.html of your react application.

   <link rel="import" href="https://stackoverflow.com/questions/26365545/./src/polymer-components/calender-element.html">
   

3. Use that element in the jsx file.

   'use strict';
   
   import React from 'react';
   
   class MyComponent extends React.Component{
       render(){
           return (
               <calender-element></calender-element>
           );
       }
   }
   
   export default MyComponent;