Passing Promo Code to Drupal Commerce via URL
There are a number of ways you could do this. Probably the best way is to use a custom module, define a menu path with a token, and do it all in PHP. But I live mostly in the GUI world. You could also do this using Rules.

I have done something similar in a 10 minute youtube video that describes how to use rules to construct a url that passes in information and does things (like adding a product to a cart, or in your case you could use it to add a discount/apply a coupon).

Video: Using Rules to create a url to add a product to cart

Step by Step


Download Rules URL Arguments 
Create a rule that fires on the event "Drupal is initializing"
Add a "Text Comparison" condition. Compare the site:current-page:path token against your first parameter "promo" for a url like "test.com/promo?coupon=123"
Add all of the actions you need to react to the rest of the parameters. In the video you'll see how to get at those parameters in the url.