REST API, iATS: How do I create a membership through the API without using CiviCRM's forms?
The iATS extension does not expose any api functions for assigning iATS "payment tokens" to contacts (not to be confused with CiviCRM tokens, a completely different thing). 

The next version of the iATS extension (1.7) will use the CiviCRM standard payment token mechanism, so you can assign them that way. 

You did check the super-awesome api explorer, yes? It makes using the api so much more fun. 

Also, if you look at this file ...
https://github.com/iATSPayments/com.iatspayments.civicrm/blob/master/CRM/Iats/Transaction.php

... you might find some useful code for your purposes.