You can try to use wp_get_archives() function.
Example from this link:
<select name="archive-dropdown" onchange="document.location.href=this.options[this.selectedIndex].value;">
<option value=""><?php esc_attr( _e( 'Select Month', 'textdomain' ) ); ?></option>
<?php wp_get_archives( array( 'type' => 'monthly', 'format' => 'option', 'show_post_count' => 1 ) ); ?>
</select>