Hi Karin,
The best approach is probably using the GPIB interface. It looks like you may need speed to transfer the data which the serial port may not be able to handle.
In either case, you can use LabView as a software to implement everything. Obtain the LV drivers for the oscilloscope. Most have at least an example of code to get you started. That is assuming that you have LV. You can also implement the code in C/C++, Visual-Basic, LabWindows-CVI. My preference is LV.
So to answer your question: YES, it is possible.
🐵
-JLV-