@Arundhati Sen Hello and welcome to Microsoft Q&A.
I understand you need to move data from a SQL DB (on-prem or azure?) to a REST endpoint which requires plaintext request body and returns JSON response body.
REST activity always uses JSON format in source and sink (or xml as source in specific cases). So, no I don't think you can use Data Factory REST connector.
You CAN use Web activity. That does work. Web activity accepts any text-based data. Binary gets tricky.
However you have to be aware of the result size limits of Lookup Activity. It only returns the first N results or 4MB. So Lookup is not always a viable solution.
An easier solution might be Logic App.
As your API returns JSON response body, I wonder if it can also accept JSON requests... Some API's can accept multiple formats.