Here is a link to the online documentation for the RightFax 10.6 Web Services API that is included with RightFax.
The method to send a fax is SendJobs
Downloadable SDK for Developers
To check and see if the API is already installed - try this URL with your server name - http://localhost/rightfax/api/help.
Replace LOCALHOST with your RightFax Server name. If the API is installed, you will see this help page.
If it isn't installed, run the RightFax Product Suite Setup on the RightFax Server and select RightFax Web API.
Here is the documentation on the SENDJOBS which is what you use to actually send a job.