I’m assuming that the custom field is associated with a post of some type.
Is would be the same principle that you did in the back-end. You enqueue a script, localized with the css file to load. Then when the script runs it can add the the stylesheet to the header. This would probably be the way you’d want it to work if you want to somehow add the stylesheed to the page during the “get_field()” or “the_field()” function calls.