Use attachment date from EXIF data on image upload.

update_image_date.php

<?php
class Unnamed_Theme {
	public function __construct() {
		add_filter( 'wp_update_attachment_metadata', array( $this, 'update_image_date' ), 10, 2 );
	}

	/**
	 * Update the 'post_date' field with the date in the image meta
	 *
	 * @param array $data The attachment meta array.
	 * @param int $post_id The attachment ID.
	 *
	 * @return array The image meta data array.
	 */
	function update_image_date( $data, $post_id ) {
		global $wpdb;

		if ( isset( $data['image_meta']['created_timestamp'] ) ) {
			// Save the original date
			$original = get_post_field( 'post_date', $post_id );
			update_post_meta( $post_id, '_original_upload', $original );

			// Update with the date from EXIF
			$wpdb->update( $wpdb->posts, array( 'post_date' => gmdate( 'Y-m-d H:i:s', $data['image_meta']['created_timestamp'] ) ), array( 'ID' => $post_id ) );
		}
		return $data;
	}

} // Unnamed Theme