This is probably not relevant for OP anymore, but I was looking for the same thing, and didn't find any clear answers, so I'll post my findings in case someone else is looking for the same.

The method you want to call to run an action is "run", as you can see in the source code here :  ​
github dot com/odoo/odoo/blob/afc47d5a95e391ec667bb696e4afc5a2cf305d84/odoo/addons/base/models/ir_actions.py#L616

So just like the other rpc calls you've been able to do, you specify these things in args under params: your_db, your_user_id, your_api_key, model (ir.actions.server in this case), the method "run", and lastly the ID of the action you want to run.

So if you send a post request to your odoo-baseurl/jsonrpc with the below body in raw/json it should work just fine:

{
​"jsonrpc":"2.0",
​"method":"call",
​"params":{
​ ​"service":"object",
​ ​"method":"execute",
​ ​"args":[
​ ​ ​"db",
​ ​ ​"uid",
​ ​ ​"api_key",
​ ​ ​"ir.actions.server",
​ ​ ​"run",
​ ​ ​id_of_action
​ ​]
​}
}