Code to make a post sticky

The sticky posts are saved as an array of post IDs in the wp_options table. Hence,

$stickies = get_option( 'sticky_posts' );
$stickies[] = $post_id;
update_option( 'sticky_posts', $stickies );

will make the post in question sticky.

EDIT:

Even better, the core provides functions to stick and unstick posts (had to have ’em).

stick_post( $post_id );
unstick_post( $post_id );

–> See source on trac