This tutorial allows you to add a text field to fill the URL of an image for each of your categories.

Add this in your functions.php file:

add_action('init', 'my_category_module');
function my_category_module() {
 add_action ( 'edit_category_form_fields', 'add_image_cat');
 add_action ( 'edited_category', 'save_image');
 }

The function to add the extra field :

function add_image_cat($tag){
 $category_images = get_option( 'category_images' );
 $category_image = '';
 if ( is_array( $category_images ) && array_key_exists( $tag->term_id, $category_images ) ) {
 $category_image = $category_images[$tag->term_id] ;
 }
 ?>
 <tr>
 <th scope="row" valign="top"><label for="auteur_revue_image">Image</label></th>
 <td>
 <?php
 if ($category_image !=""){
 ?>
 <img src="<?php echo $category_image;?>" alt="" title=""/>
 <?php
 }
 ?>
 <br/>
 <input type="text" name="category_image" id="category_image" value="<?php echo $category_image; ?>"/><br />
 <span>This field allows you to add a picture to illustrate the category. Upload the image from the media tab WordPress and paste its URL here.</span>
 </td>
 </tr>
 <?php
 }

Function to save :

function save_image($term_id){
 if ( isset( $_POST['category_image'] ) ) {
 //load existing category featured option
 $category_images = get_option( 'category_images' );
 //set featured post ID to proper category ID in options array
 $category_images[$term_id] =  $_POST['category_image'];
 //save the option array
 update_option( 'category_images', $category_images );
 }
 }
}

To display the image put this in “category.php” or “archive.php” depending on your theme, it’s better to choose “category.php”,  and add this code before the WordPress loop :
:

<?php
 if(is_category()){
 $category_images = get_option( 'category_images' );
 $category_image = '';
 if ( is_array( $category_images ) && array_key_exists( get_query_var('cat'), $category_images ) ){

$category_image = $category_images[get_query_var('cat')] ;
 ?>
 <img src="<?php echo $category_image;?>"/>
 <?php
 }
 }
 ?>