Convert an theme options page to use in customize.php also?

You need to add a control to it.

function mytheme_customize_register( $wp_customize ) {

  $wp_customize->add_section( 'mytheme_options', 
     array(
        'title' => __( 'MyTheme Options', 'ppr' ),
        'priority' => 35,
        'description' => __('Allows you to customize some example settings for MyTheme.', 'ppr'),
     ) 
  );

$wp_customize->add_setting( 'link_textcolor', array(
    'default' => get_option( 'your_theme_page_option_value' ), THIS IS THE OPTION NAME YOU CREATED WITH YOUR OPTIONS PAGE CODE
    'type' => 'option',  // FOR OPTIONS USE OPTION
    'capability' => 'edit_theme_options',
    'transport' => 'refresh', // WILL REFRESH INSTEAD OF JS. YOU HAVE TO WRITE JS TO MAKE UPDATE INSTANT... ITS A PAIN IN THE ASS http://codex.wordpress.org/Plugin_API/Action_Reference/customize_preview_init
) );


// THIS IS WHAT YOU WERE MISSING
$wp_customize->add_control( new WP_Customize_Color_Control( $wp_customize, 'link_color', array(
    'label'        => __( 'Link Text Color', 'ppr' ),
    'section'    => 'mytheme_options', // ID OF SECTION ABOVE
    'settings'   => 'link_textcolor', // ID OF SETTINGS ABOVE
) ) );

}
 add_action( 'customize_register', 'mytheme_customize_register' );

Alex make sure you are including the options in your templates otherwise you wont see any changes. For example if you want to us the options in all templates make sure you are actually putting the option inside the header or all the files that will need changes.

So for the above code I would use something like this and place it in my header.php or even just in a function that uses the wp_head action if it’s for styles.

function mytheme_customizer_styles() {
        $link_text_color = get_option('your_theme_page_option_value'); // THIS IS THE OPTION VALUE THAT YOU CREATED WITH SETTINGS API AND YOUR CUSTOM OPTIONS PAGE AND IS ALSO THE NAME OF THE OPTIONS DEFINED IN THE `add_setting` field above.
    ?>
    <style type="text/css" id="mytheme-customizer-admin-header-css">
         .link-text-color { color:  <?php echo $link_text_color; ?>; }
    </style>
    <?php
}
add_action( 'wp_head', 'mytheme_customizer_styles', 9999); // JUST MAKE SURE THE PRIORITY IS LATE ENOUGH SO ITS NOT OVERRIDEEN