BrE native, not a teacher
In British English we would say "To pick up the phone"
Note that this could be to make, or to answer, a call. If the phone is ringing, you would say "pick up the phone" or "answer the phone".
In BrE, you "take a call" (meaning to accept it). "Pick up the call" isn't wrong, but in offices, it usually means to use your handset to pick up a call on a colleague's phone (for example if they are not there).