API to add a custom rule to a specific site

I don’t fully understand your question nor your use case.

But you can try this API to assign/reassign a phone number to a site.

Hi Phong,
Apologies i should explain better,

I need the ability to quickly add and edit call handling rules for a site. It can be done as a company but i can't figure out if it's possible to select the site itself. 

You can read site call handling rules using this API. Read the sites and use the site id of a site as the [extensionId].

Then call update call handling API to change/edit.

Yes but that requires one to be added to each site, my assumption is we cannot add one? 

So confusing. Here is what you asked “I need the ability to quickly add and edit call handling rules for a site.” and now you said “one to be added to each site” ???

“I need the ability to quickly add”
Editing rules I understand can be done but adding a new one for a specific site?

Not sure what's confusing? It doesn't matter if it's one or Mutiple, id still need to run a separate API call for each rule ID

There are many APIs under the Call Handling Rules section. Next to the Update API is the List, Create, Delete etc.