You can just use urlopen or requests and than read json as a dataframe using spark.json(). Problem is that in that case you will need handle whole logic (when to load data, how to handle incremental load etc).

Easier solution o is to use streaming and put kafka with data from your API ( confluent.io can be registered also through Azure) or any other stream like eventHubs and than your newest data can be read as kafka stream in databricks and processed data will be saved in destination of your choice. Maybe on side of your infrastructure you can just deploy microservice which read from rest apis and save to stream.