In this context, "as it was" is comparing what the application does (establishes an audio path) to how phone calls were traditionally made (by a human physically picking up the phone's receiver). The application cannot physically pick up the phone. Furthermore, there is no phone for it to pick up, even if it could. A few commas may have helped. For example: The answer application picks up the phone, as it was, by establishing an audio path to the calling party. Quotation marks could have been used, too, resulting in "as it was" not even being needed. For example: The answer application "picks up the phone" by establishing an audio path to the calling party. Finally, you will probably see "as it were" more often than "as it was", even if it may not always be grammatically correct.

This sentence has a parallelism issue. It should be either The answer application [picked] up the phone as it was... or The answer application picks up the phone as it is... "as it is"- [it]'s current state of being. "as it was"- [it]'s former state of being. Example: These items are being sold "as is". The seller is making clear that there is no promise that the items are in good condition by using "as is". Example: As it was, I didn't have the energy to do my homework. At a former time, the writer's condition was very tired.