How to add an id element to a field in Drupal 7
First of all are you using the Link module? Just so we know.

I would create a template to the field:

You can copy the /modules/field/theme/field.tpl.php to your theme, change the name to field--field-print-link.tpl.php and customize it in any way wanted.

Don't forget to flush your caches!

Or, of course, you could add the id with JS using a bit of jQuery (as Drupal already uses it):

$('element').attr('id', 'value');