By default, your Strutta contest or sweepstakes site will be accessible on mobile devices for viewing and interaction whether it is launched as a Standalone Microsite or embedded in your website (iframe).
If you are running your promotion as a Facebook Page Tab users will not be able to view it on mobile from your Facebook page.
Facebook do not support any third party tabs on mobile and do not have any plans in the future to do so.
As a workaround you can post the direct link (http://promo.com) or the direct iframe link to your Facebook page so users on all devices can access it. Desktop users will still be able to access the promotion as a page tab by clicking the tab on your Facebook page.
Tips: You can shorten this URL if it is too long to post on your Timeline. 'Pin' the post to your Facebook Timeline so it stays at the top of your page for seven days, giving the post maximum visibility.