You can do this with a durable function which is a specialized Azure Function. Logical apps can also do it. The differences boil down to how much integration and customization you want. Refer to this doc on the official differences.
In both cases you define a storage trigger that monitors the container you care about. When a blob is added or updated in the container then the trigger is fired and Azure spins up your DF or LA.
- Create a new DF/LA in Azure. The recommendation is to use consummation model.
- The DF/LA will either directly contain the logic to process the request or call out to an API that does.
- Add a storage trigger that points to the container you want to monitor. For logical apps you can see the instructions here.