برای اینکار بصورت زیر عمل می کنیم:

class myForm extends React.Component {

constructor(props) {
    super(props);
    this.state = {selectedOption: ''};

handleOptionChange: function (changeEvent) {
  this.setState({
    selectedOption: changeEvent.target.value
  });
}
render: function(){
           return (
<form>
    <div className="radio">
      <label>
        <input type="radio" value="React" 
                      checked={this.state.selectedOption === 'React'} 
                      onChange={this.handleOptionChange} />
        React
      </label>
    </div>
    <div className="radio">
      <label>
        <input type="radio" value="JSF" 
                      checked={this.state.selectedOption === 'JSF'} 
                      onChange={this.handleOptionChange} />
        JSF
      </label>
    </div>
    <div className="radio">
      <label>
        <input type="radio" value="JavaScript" 
                      checked={this.state.selectedOption === 'JavaScript'} 
                      onChange={this.handleOptionChange} />
        JavaScript
      </label>
    </div>
  </form>
 )
}