Reading RFID tags with Arduino IDE, not using Arduino
Short answer:
NO

Long Answer:

Option 1:
 Use a USB RFID reader and create a basic processing/python/ app to read from the USB RFID reader and post it where ever you want it to

Option 2:
Use the arduino to read from the ID-20LA and send the data via UART to your computer and then create a windows app using processing/python/ to send it to your API endpoint

Option 3: 
Use the arduino YUN to read from the ID-20LA and then create a basic python program to run on the YUN itself. Such that it will read data from the atmel microcontroller (on the YUN) and post it to your API endpoint. This is a much cleaner yet slightly more expensive way of doing this.