namespace WpfBindRadioButtonToEnum.Models
{
    public enum Gender
    {
        Female,
        Male
    }
}

using System;
using System.Globalization;
using System.Windows;
using System.Windows.Data;

namespace WpfBindRadioButtonToEnum.Converters
{
    public class EnumBooleanConverter : IValueConverter
    {
        public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
        {
            if (Enum.IsDefined(value.GetType(), value) == false)
                return DependencyProperty.UnsetValue;

            return Enum.Parse(value.GetType(), parameter.ToString()).Equals(value);
        }

        public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
        {
            return Enum.Parse(targetType, parameter.ToString());
        }
    }
}

using System.ComponentModel;
using WpfBindRadioButtonToEnum.Models;

namespace WpfBindRadioButtonToEnum.ViewModels
{
    public class MainWindowViewModel : INotifyPropertyChanged
    {
        Gender _genderValue;
        public Gender GenderValue
        {
            get { return _genderValue; }
            set
            {
                _genderValue = value;
                notifyPropertyChanged("GenderValue");
            }
        }




        #region INotifyPropertyChanged Members
        public event PropertyChangedEventHandler PropertyChanged;
        private void notifyPropertyChanged(string propertyName)
        {
            if (PropertyChanged != null)
            {
                PropertyChanged(this, new PropertyChangedEventArgs(propertyName));
            }
        }
        #endregion
    }
}

<Window x:Class="WpfBindRadioButtonToEnum.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:VM="clr-namespace:WpfBindRadioButtonToEnum.ViewModels"
        xmlns:C="clr-namespace:WpfBindRadioButtonToEnum.Converters"        
        xmlns:Models="clr-namespace:WpfBindRadioButtonToEnum.Models"
        Title="MainWindow" Height="350" Width="525">
    <Window.Resources>
        <VM:MainWindowViewModel x:Key="VMainWindowViewModel" />
        <C:EnumBooleanConverter x:Key="CEnumBooleanConverter" />
    </Window.Resources>
    <StackPanel DataContext="{Binding Source={StaticResource VMainWindowViewModel}}">
        <TextBlock Text="Gender" Margin="3" />
        <RadioButton Content="{x:Static Models:Gender.Male}" 
                     IsChecked="{Binding GenderValue, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged, 
                                Converter={StaticResource CEnumBooleanConverter}, 
                                ConverterParameter={x:Static Models:Gender.Male}}"
                     Margin="3" GroupName="G1" />
        <RadioButton Content="{x:Static Models:Gender.Female}" 
                     IsChecked="{Binding GenderValue, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged, 
                                Converter={StaticResource CEnumBooleanConverter}, 
                                ConverterParameter={x:Static Models:Gender.Female}}" 
                     Margin="3" GroupName="G1" />
    </StackPanel>
</Window>