I need to transfer 1 million rows over the internet using Web API and JSON

I am working on a project where I need to transfer about a million rows from our third party server to our server.

The criteria are 1. I cannot have direct database access. 2. The data should be available on demand and do not want to store the data for a long time locally. 3. I am not allowed to transfer files.

I was thinking of using Web API for this job and transfer the data using JSON. Along side with this I was going to make the service async. I have also look at Signal R and see if that would work. However that would lead me to storing the data locally which is against one of the criteria.

Question is that, is Web API the answer to my problem or is there a better way of achieving the end result.